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.

A lot of people think it's irrational to vote if your vote isn't going to have an effect on the outcome. I live in an extremely blue district of a slightly red county in a very blue state. In local and statewide elections, my vote has so little an effect that it's not worth voting if the only point of voting is for my one vote to have an effect on the outcome. New York is overwhelmingly going to continue to support Senators Schumer and Clinton, and they tend to vote Democratic in governor elections except when there's a very moderate Republican like George Pataki on the ballot. County-wide races are closer, and so is the U.S. House district, which was almost a toss-up in 2006. Things were even more one-sided when I lived in Rhode Island.

But it simply isn't true that voting is only worth doing if you're going to be the deciding vote. There are other reasons people give for voting, some better than others. One that often occurs to me when it seems hopeless for my candidate is that if everyone voting for the other side thought it wasn't worth voting because the outcome is assured then my candidate might have a chance. Other reasons include that it helps you psychologically to feel like you're contributing and that it's simply your obligation to do what you can to influence things for the better even if what you can isn't by itself going to make the difference in who wins the election.

Any of those responses would be sufficient by itself, except perhaps the psychological benefit one (at least if that involves self-deception, and if it doesn't then it's not a distinct reason but depends on one of the others). I think there's an even better reason to vote, and I think it might actually be what motivates me most, but I hadn't actually thought about it in these terms until today. It takes a page from Calvinist responses to the objection that if the future is already determined then there's no point in praying.

Calvinists come in several varieties, but the most common sort of Calvinist (which isn't the same as being the most noticed kind on the internet) is compatibilist about human freedom and divine predetermination. If God has a plan that includes everything I'm going to do, everything every other person is going to do, and an outcome for every prayer I ever pray, then is it worth praying? My prayer isn't going to change anything, after all. Of course, my prayer would also be in this plan, and if I didn't pray then a different outcome may well have been in the works. Compatibilists about divine predetermination and human action are going to insist that God works through our choices and doesn't just force things outside our control. Our prayers are part of how God's plan works itself out as history unfolds.

One thing Calvinists sometimes say is that praying is not so much for the outcome but for us. God wants us to pray because of what God will do in us because we pray. I don't want to deny that, but it's certainly not the emphasis in scripture on reasons to pray. The emphasis seems to be on two things. One is that prayer does affect things. It doesn't change them, because the future can't be changed anymore than the past or present can. If the future is a certain way then it can't be changed. Even open theists don't think the future can be changed. Why should someone who thinks there's a definite future think it can be changed? But for the reasons in the previous paragraph, the future can be influenced. It can be caused by things in the present, and I can be part of that process of bringing it about. A compatibilist should have no trouble saying that sort of thing.

But there's another reason in scripture for why we should pray, even though God has worked out the end from the beginning, and this one (unlike the previous one) does have some relevance for voting. God wants us to communicate our dependence on him and to express our desires to him. He wants us to see him as the Father who cares for us and meets our needs and our wishes, provided that our wishes are righteous and as long as there isn't some other reason beyond our ken for why God wouldn't grant a particular wish (as there may well be). As Jesus points out, what father when presented with a request from a child for bread or fish will give a snake? God wants to bestow good things on his children and delights when we come to him with requests, for the same reasons a giving parent delights in such things. Given that, it's a privilege to call him Father, which is why it's a big deal that Jesus starts out the Lord's prayer with "our Father". Those who don't avail themselves of that title in addressing him are missing out on something great. Those who don't address him at all are missing out on even more.

The same dynamic plays out in a smaller way with voting. I'm privilege to live in a country that seeks my opinion on who should occupy certain offices. Even if my vote doesn't have an effect in putting someone in office, it's a privilege to be able to contribute my thoughts in the process of the communal decision that an election involves. I don't believe voting is a moral right. But I think I'd be wasting an opportunity to express my opinion if I didn't vote, and wasting a privilege is at least unfortunate (and I would even argue that it's immoral). This seems to me to be a much better reason to vote than any of the more common ones that I hear, even if most of them are good enough reasons.