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.
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.
Jeremy Pierce is a philosophy professor, Uber/Lyft driver, and father of five.