There are several different things someone might mean when they speak of imposing religious beliefs on those who don't hold them. There are two different axes to pay attention to. One is what is meant by "imposing", and the other is what is meant by "religion".

On the first axis, what is meant by "imposing", I can think of a number of things in decreasing order of severity:

1. Forcing people with threat of force or imprisonment
2. Coercing people by some manner less severe than force or threat of imprisonment (e.g. giving them incentives like a right to vote, to drive, to hold an independent job) that most Americans consider rights or close enough to it
3. Incentivizing by some manner less severe than coercion (e.g. government influencing social acceptance, giving tax credits or deductions, criminal penalties of smaller sort such as a fine)
4. Calling on people to change their mind or behavior, perhaps with strenuous argumentation
5. Explaining one's attitude on the issue
6. Simply stating what one's view happens to be

On the second axis, what is meant by "religion", I can again think of a number of things, in decreasing order of centrality to religion:

A. espousing a statement of faith or unfaith (that they might not actually agree with)
B. engaging in certain behavior that is motivated (on the part of those instituting the policy) merely by religious beliefs and not by any attempt at rational argument
C. engaging in certain behavior that is motivated (on the part of those instituting the policy) in part by religious beliefs but also by some attempt at rational argument, even if it's not a strong argument
D. engaging in certain behavior that is motivated (on the part of those instituting the policy) in part by religious beliefs but is held by most who hold it (even if controversially) by rationally-motivated arguments that, while disputed, at least are philosophically-driven in addition to or, for some, without the religious motivation
E. engaging in certain behavior that is motivated (on the part of those instituting the policy) in part by religious beliefs but is commonly held by most people, and for most people there is motivation that in their minds is on grounds entirely independent of religion

There are those who insist that even stating one's religious views counts as imposing them in an improper way, never mind preaching them. Fortunately, in the United States even 4A is protected speech by the first amendment. I'm not about to argue for 1 either, so we're really looking at 2 and 3. In the history of the world, we've certainly seen pseudo-conversions coerced at swordpoint or recantations of religious beliefs at the threat of martyrdom. In comparison with that, the idea that one is imposing one's religion merely by trying to make a case for it seems absurd. It's similar to the War on Christmas people complaining of Christians being persecuted in the United States just because schools are refusing to sing Jingle Bells in schools on the ground that the song is tied to a religious holiday. (In my experience, schools nowadays don't reduce Christian content at Christmas but simply include it alongside religious content for other religions' holidays too, so this complaint is getting even more stale than it was when I was younger, when such songs might have been excluded on the strange claim that they're somehow religious).

We do have some laws that are all the way down to 1E or sometimes 1D, however. For example, same-sex sodomy laws, bans on selling contraceptives, and bans on teaching evolution (all deemed unconstitutional now) were often religiously-motivated but did include arguments, often arguments widely accepted at the time, that didn't rely on religious premises. Evolution was thought not to be as well-supported as its proponents think. Creation science has insisted that evolution is just bad science. This isn't about whether their arguments are good but about what kind of arguments they are. Similarly, bans on same-sex sodomy were justified more by disgust at such acts than any biblical prohibition on them, and the Connecticut ban on selling contraceptives was supported by an argument about population control.

But there remain some laws at level 1E or 1D and some attempts at instituting laws at this level. Sodomy laws are deemed unconstitutional by the Supreme Court since 2004, but incest laws vary from state to state. It's not criminal in Rhode Island to have sex with a close relative, but you can't marry them unless you're Jewish (to allow for Levirate customs, I assume). In Ohio it's criminal to have sex with your children, but only the parents are criminal even if the children are adults. But in Massachusetts you can get 20 years in prison for having sex with your adult sibling, even if one of the two parties is demonstrably infertile or if it's a same-sex act, in either case removing any chance of genetic problems with offspring. Such a law is, as far as the courts have so far indicated, perfectly constitutional. Yet I can think of no easy argument against it unless you rely on beliefs that are either very controversial and often supported by religion or simply feelings of disgust. Arguments against pornography aren't all religious (see the feminist arguments), but we make distributing or producing certain kinds of pornography illegal in part because a lot of people have religious objections to it. (But I should say that this is clearly 1E and not 1D, since almost all religious people who object to pornography would agree with just about the entire feminist case against pornography, despite feminist claims to the contrary.)

In fact, 1E prohibitions occur all the time. Laws against murder or robbery fit into this category. People certainly have religious reasons for thinking such acts are wrong and ought to be given severe penalties. But the arguments for them are widely accepted by religious and non-religious people, and the secularly-accessible arguments are usually present even for religious people.

Coercion of sorts 2 and 3 is a little more commonly thought of as imposing religion, and there are some ways that can occur today in the United States with legal sanction (although for letters further down the list than happens with Islam). You're not going to find 2A or 3A in the U.S. today, but you will find both in Islamic countries. Most debates in the political context of the U.S. about imposing religion aren't even about 2B or 3B. The kinds of things that get labeled as Taliban-like behavior in the U.S. aren't about matters that have purely religious support. They at least make an attempt at rational argumentation. But that's also true of the Islamic laws requiring women to wear veils or prohibiting girls from being educated in any formal way. The supposed rational argumentation in both cases is extremely weak and based on false views of the capabilities of women or false priorities, elevating the concern with provoking male lust to a point where it overcomes eminently reasonable considerations about freedom in how women might dress and conduct themselves in public. Even the most stringent Christian concerns about modesty in women's dress are going to allow for much more freedom than you'll find in many Islamic prohibitions on female dress.

I think most cases I'm aware of on level 2 are actually all the way down to 2E. I'm thinking of laws that prohibit minority religious behavior, such as requiring a photo ID for a driver's license (which some orthodox Jews resist and even some Muslims, or like the Florida law requiring a photo ID not to have a face covered too much, which some Muslim women won't do). The attempted ban on peyote even in Native American religious ceremonies would have fallen into this category, but Supreme Court, in an opinion by Justice Scalia, overturned that. Banning certain kinds of political protests that someone might have religious reasons for insisting on doing, e.g. perhaps an abortion protest of a certain nature, amounts to a 2C imposition.

Level 3C is much more fair game for a lot of issues in the U.S. We don't imprison people for much at level C, but we do incentivize religious charitable giving by giving tax deductions, and we recognize (so far) a privileged position for opposite-sex unions to be called marriage at the federal level and in most states. That gives government sanction for something with some secular arguments but also based on religious motivation for many supporters of that policy, and it has an effect of cultural sanction or respect for certain behavior over other behavior. If we ban a certain religious act but without criminal penalty other than a fine, that would fall under 3C. There are religious and non-religious arguments for abortion protests that cross the line into illegality to a point of a fine but not to the point of imprisonment.

In the UK and Canada in the last couple years, pastors have been carted off to prison for preaching that same-sex sexual acts are immoral. This isn't quite an expectation of having a certain view, but it's prohibiting the speaking of such a view. It's a level 1 prohibition of level 6 behavior. Americans rightly deride such policies as contrary the value of debate as a basic, fundamental component of civil society. Speech codes that prohibit even stating your religious views if such views are considered offensive to someone, while indisputably unconstitutional in the United States, somehow manage to appear at most universities anyway. Even 4A is uncontroversially protected speech under the first amendment, unless it takes it to a level of actually provoking people to a fight or to the level of panic that would result by yelling "fire" in a crowded theater. Yet I've encountered a number of people who have considered it a clear case of immorally imposing one's religion, as if trying to persuade someone of a view you happen to find true is somehow wrong. Some take it to a further extreme, considering even the reporting of your view to be inappropriate when it's a controversial view that some might find offensive. Merely indicating that one believes Jews who don't accept Christ as the Messiah will go to hell would, to some people's mind, count as imposing one's religion in an immoral way. I find such an analysis so unhealthy that I almost consider it undeserving of a reply. But if pressed I would insist on the value of philosophical debate, the importance of understanding those who disagree with you, and the moral importance to certain religions of attempting to win people over to something they consider very urgent for all humanity, which prevents them from remaining silent if they're taking their own religion seriously.
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What's the moral of the story? Mostly what motivated me to work through all this is that I think we should be wary of anyone who makes blanket statements about imposing religion, whether moral statements or simply factual claims that it has happened. It should be pretty clear from all this that it's never clear what people mean by that unless the specify, and the debate that might ensure once they do specify is probably worth having. Most people who make such comments haven't thought them through and could benefit from some effort to explore precisely what they mean. The term "imposing religion" is at this point so unhelpful as to be worth avoiding whenever we can, and in its place let's clarify the particular elements that we're concerned about, since the different items in both lists above certainly do involve different moral considerations.

I've been trying to put Norman Geisler's normative theory on the map of positions I'm aware of, because I think he makes a genuine contribution to the field, and he's been pretty much on the sidelines in terms of ethical theory given that he's only published with Christian publishers for Christian audiences. He calls his view Graded Absolutism, which I think is a misleading term (and arguably a misapplication of the term, depending on how he means it).
Here are four views along a spectrum:

1. Consequentialism (Jeremy Bentham, John Stuart Mill, G.E. Moore) -- consequences are the only determinant of whether an act is right or wrong; genuinely moral principles never conflict, because there is only one -- to seek the best consequences [but much of the work is determined by what counts as the best consequences, with utilitarians focusing only on pleasure and pain and more comprehensive consequentialists including many other consequences)
2. Rossian deontology (W.D. Ross) -- several moral principles are relevant, and consequences play a role as one of them; different principles take precedence in different situations
3. graded absolutism (Norman Geisler) -- several moral principles are relevant, but not consequences; the same hierarchy of importance exists for these principles no matter the circumstances
4. Kantian deontology (Immanuel Kant) -- moral truths are absolute in the sense that they never have exceptions, no matter how serious the consequences are; moral principles never conflict

Consequentialism and Kantianism are absolute in the sense philosophers usually mean when they use the term about an ethical theory. Moral rules are absolute, and there is never any genuine conflict between them. There is at least one moral principle with no exceptions for consequentialists, because there is only one, and it never has exceptions. For Kant, there are several principles, but he thinks they will never conflict. Deontologists think either that there are more principles that matter than just consequences (as Ross thinks) or that consequences are entirely irrelevant (as Geisler and Kant think). Many deontologists find Kant's view implausible, because there are often cases where moral principles conflict. But they also want there to be moral principles besides just consequences. Ross and Geisler offer different views on what happens next.

According to Ross, there are sometimes several moral principles that play a role in a given case, and one of them will take precedence in each case. But it's not according to a pre-existing hierarchy. Sometimes the situation will make one principle more appropriate than another, but in a different situation the hierarchy is reversed. Perhaps the lying principle is more important than the principle of seeking the best consequences when not much is at stake in terms of consequences. It might make things a little better in the world if you tell a lie, but the principle against lying is more important when the difference in your self-interest and the interest of others is not much changed whether you lie or not. But in a case where hundreds of lives are at stake, the principle of not lying becomes less significant than the principle of promoting the good of others (which is a consequence). When I teach ethical theory, I teach consequentialism and Kant and then present Ross as a moderating position, taking aspects of each but rejecting other aspects of each. Geisler seems to have found a different moderating position along this spectrum, one that's closer to Kant in two respects than Ross's view is.

One Kantian element Geisler wants to retain that Ross rejects is in not counting consequences at all. There might be cases where lying is all right, according to Geisler, if a more important moral principle is at stake. But that principle won't be framed in terms of consequences, and how serious the consequences are plays no role in the moral status of the action. (On this point, I side clearly with Ross. Of course consequences can play a role in determining how good or bad an action is, even if they are not always decisive.)

Second, Ross thinks which principle is more important will vary from situation to situation. Geisler doesn't like that. He wants a rigid hierarchy that is the same in every case. The only thing that determines which moral principle applies is which ones are relevant, and then you go with the highest one in the list that's relevant. This is in fact why Geisler misleadingly calls his view absolutist and why he would not think Ross's views is absolutist. What is absolute is the structure of the moral hierarchy. That never has exceptions and doesn't vary from situation to situation. But only the very top moral principle is absolute, strictly speaking, because the others all allow for exceptions. So it's not absolutist about most moral principles, like Kant's view, just about the top one and about the relative positions of all the moral principles in the hierarchy. Most ethicists who speak of absolutism are thinking in terms of whether moral principles in general are absolute, and Geisler's view would say no to that. But if absolutism is the view that at least one moral principle is absolute, then Geisler would agree with that. The top moral principle in the hierarchy is absolute.

I want to distinguish both of these moderating positions from a number of views that they get confused with fairly easily. First, there's situational ethics. Situational ethics is itself often confused with relativism. Situational ethics in reality is a consequentialist position that takes love to be the only important consequence. It is not relativism, and neither is consequentialism in general or utilitarianism in particular, despite all these views sometimes being called relativism.

The views most commonly called moral relativism are meta-ethical views about the nature of moral language. They find ways to account for moral language without there being objective moral truths. Subjectivism says what's right is just whatever the individual person considers right. Cultural relativism says what's right is whatever your culture says is right. Emotivism says there are no truths or falsehoods about right and wrong, and attempts to say something is right or wrong are more like expressing your approval (they mean, roughly, things like "Hooray for helping people out!" and "Boo! Abortion!" but don't express any content that can be true or false). There are other variations, but what all these views have in common is that there is no truth or falsity of moral statements except, possibly, to express truths about the person making the statement or about that person's culture.

Sometimes an incoherent view common among college students is called relativism. This view is basically an inconsistent combination of one of the above meta-ethical views (usually subjectivism or cultural relativism or an inconsistent adoption of both) with the moral absolute that we ought not to criticize other people's moral views or other culture's moral views. I don't consider that a genuine view, just a confusion and an attempt to combine incompatible claims.

But the views I'm talking about here are very different from what's usually called relativism. They are not situational ethics, because they are not consequentialist, and situational ethics is a consequentialist theory involving love as the only important consequence. They are not meta-ethical relativism. The meta-ethical position they endorse is objectivism. The moral principles for Ross and Geisler are objectively true. It's just that sometimes one principle is more important than another (for Ross) or some principles are always more important than certain others (for Geisler).In both cases, the facts that determine which principles are relevant in a case are objective. For Geisler, the hierarchy of principles remains constant across situations. For Ross, it doesn't. But even for Ross there are objective facts about the situation that make certain principles more appropriate for that situation than other principles. Contrast the view that your psychological makeup, moral views, or cultural background is what determines which principles are important. These views are not relativism but genuinely objectivist moral theories.

Alan Turing famously devised the Turing test, which was intended to test whether a machine can think. If it could show enough behavior consistent with thinking, Turing claimed that it really does think.

Turing tests have come under quite a lot of criticism for relying on the fallacious inference from something appearing to have a certain property to the conclusion that it does have that property. Turing tests take the behavior that follows from genuine thinking to be sufficient to establish that there is such thinking, even if the same behavior can be produced by a computer program. I would take the fact that it comes from a computer program to be sufficient reason to think such behavior can occur without genuine thinking.

So the usual criticism of Turing tests is that they assume thinking is occurring just because the usual behavior resulting from thinking is occurring. While I'm not interested in diminishing that objection, it occurred to be recently that Turing tests aren't just not sufficient for thinking (things that pass the test might not be thinking). They're not even necessary (things that think might fail the test). For one thing, someone who thinks might simply refuse to comply with the test and thus could fail. But more poignantly, someone with a communication-related disorder, e.g. someone with autism and dyspraxia who is completely non-verbal, simply cannot display the behavior the test is looking for. Being unable to communicate is certainly not a sign of being unable to think.

I would argue that more harm is caused by those who take passing a Turing test to be necessary for intelligent thought than is caused by those who take passing such a test to be sufficient for intelligence. We recently attended a communication seminar for parents and educators of non-verbal and mostly non-verbal children. At one session an autistic college senior was present. He can now speak in a somewhat limited manner, but he can communicate by typing on a portable device at a level that's almost certainly far beyond what most kindergarten teachers would have ever expected if they had seen his communication level in his younger years. He had no verbal language until age 12, but because his teachers taught him to type they knew that he was able to grasp much higher levels of thought than most teachers would have even speculated. At last night's session, there was a guy with Down Syndrome and autism who, as far as I could tell, can even as an adult do little more than grunt was typing out sentences that indicate a pretty high-level grasp of some pretty abstract and complex phenomena.

With a son who can't speak much more than five syllables at a time (unless he's singing or engaging in echolalic repetition of Veggie Tales or some other TV show), we've been able to see something like this firsthand. We knew in kindergarten that he was reading fairly complex words for the level of verbal behavior we normally saw, because he'd occasionally see a word and say it. (I remember him saying "banana" one time when there were no pictures of a banana, just the word.) But it's been very hard to get him to demonstrate his intelligence with writing, until this year, with his teacher and support staff working very hard with him to get him typing. Six months ago we could get him to trace over words we wrote out with a highlighter, or we could get him to point to words sometimes on a communication device, which could then pronounce them for him (but they had to be programmed in first, since he wasn't typing them). Now he's showing reading comprehension by completing "because" clauses to answer why certain characters did certain things. It makes me wonder how much he's been wanting to be able to communicate for years but unable to get his mouth or hands to do anything to show it.
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The Turing defender might now say that he is able to show it, so it's not an objection to the test, but he's only now able to show it, and there's no reason to think he just started to be able to think on this level. I suspect most teachers would have assumed he couldn't handle the level of math that he's doing (basically right on second grade level) or the vocabulary and reading that he's doing (which is, as I said, at a pretty good level for demonstrating reading comprehension, better than his older brother could demonstrate at that age). He happens to have a teacher with 25 years of experience working with kids like him, who is informed about technology and methods to get kids like him communicating. Many educators encountering a kid like him might well assume low ability levels and not work to get him to communicate. In effect, they're using a reverse Turing test and concluding that someone isn't intelligent because they can't show it in the typical ways.