Once again, the unholy wars have broken out here at Scienceblogs. The latest skirmish got started when Matt Nisbet put up an article titled "ATHEISM IS NOT A CIVIL RIGHTS ISSUE." In this article, Nisbet claims that atheists don't face a civil rights struggle, but merely "a public image problem." Many of the comments left over there have argued with that basic point, as have PZ, Jason Rosenhouse, Mark Hoofnagle, and other Sciencebloggers. Personally, I think Nisbet is right on this one - but only if the term "civil rights" is defined so narrowly that it loses most of its meaning.
There is certainly no doubt that atheists in America have a public image problem. Actually, given the polls that have come out suggesting that less than half of Americans would vote for an otherwise well-qualified atheist who belonged to their own party, I'm not sure that "public image problem" really does the situation justice. At a minimum, it's an understatement that's in the same league as calling pedophilia a minor social deviation.
If we define "civil rights" as the rights that a group is promised under the law, then atheists do not have a civil rights problem in the United States. Under the Constitution, there can be no establishment of religion, and this has generally been interpreted by the courts (at least in recent decades) to mean that the government is also prohibited from favoring religion over a lack of religion. Unbelievers are promised the same treatment as believers, so there is no civil rights problem.
Of course, under that logic, the civil rights movement should pretty much have been over once the voting rights act was passed and the segregation laws were ruled unconstitutional. Feminism should have wrapped things up once women got the right to vote. That didn't happen, of course, in either case, because most of us are capable of recognizing a simple, unpleasant fact: your rights on paper aren't necessarily the same as your actual rights.
Atheists, unfortunately, do face a great deal of discrimination. Actually, I should rephrase that. The discrimination is not faced by all atheists. It's faced by those people who, for whatever reason, choose to publicly identify themselves as nonbelievers. For one set of examples, you need look no further than child custody cases. Volokh has a laundry list of appeals court cases dealing with child custody. In all of these cases, judges - people sworn to uphold the Constitution - decided that a religious upbringing is "in a child's best interest," and used that as a factor in restricting custody rights of non-religious parents. There are plenty of other examples, many cited in the posts I linked to in the first paragraph.
I'm not trying to evoke (or, for that mater, spark) anything comparable with Selma, Alabama, but I think that when you have judges berating you for the damage that your lack of belief does to your children, you're talking about more than just a public image problem. The legal protections are there, so atheists don't face wholesale, legalized discrimination. That's good, but there are still a hell of a lot of retailers out there.