The Becket Fund for Religious Liberty is supporting Arkansas state Representative Richard Carroll's effort to repeal a state constitutional provision that bans any “person who denies the being of God” from holding public office or testifying in Court.
As the Becket Fund press release linked above points out, it is unlikely that this constitutional provision - or others like it still on the books in several other states - could actually be enforced. Any effort to do so would almost certainly be invalidated by the courts as a violation of the First Amendment. Nonetheless, repealing the law will have some symbolic value in signalling that the state government recognizes atheists as equal citizens of its own volition, and not merely when compelled to do so by the courts.
At the same time, it is important to remember that archaic legal restrictions are far from being the main obstacle to office-holding by atheists. Although atheists constitute some 3 to 9 percent of the American population and are a generally well off and well-educated group, there are no openly atheist members of Congress [correction: there has been exactly one such congressman in US history], governors, or cabinet members, and only a tiny handful of state legislators. The principal reason for this is the widespread public prejudice against them, which is greater than that against any other ethnic or religious group on which we have polling data. For example, as discussed in last link, some 53% of Americans would categorically refuse to vote for a "qualified" atheist candidate for president nominated by their own party, as opposed to 43% who would refuse to vote for a qualified gay candidate of their party, 38% who categorically refuse to vote for a Muslim candidate, 24% for a Mormon one, and single digits who refuse to vote for blacks, Catholics, or Jews. For reasons I went into in detail in this article and this series of posts, such blanket hostility to atheists is unjustified. A 2004 poll found that 51% of Americans think that “[i]t is necessary to believe in God in order to be moral and have good values."
Hostility towards atheists is perhaps the last form of crude religious prejudice still accepted by a majority of the American population. Repealing the Arkansas law and others like it won't change that. But it would be a small step in the right direction.
UPDATE: Actually, there is one openly atheist congressman - Pete Stark of California, whose public announcement about his atheism I blogged about in 2007. This made him the first openly atheist member of Congress in American history. As I pointed out at the time:
Stark's announcement is not much of a counterexample to my argument that atheists are severely discriminated against in the political arena . . . Stark is a well-entrenched incumbent in a heavily Democratic district and is probably nearing the end of his career (he is 75 years old). He therefore is running a much smaller political risk than would most other politicians if they made a similar statement. Although Stark's announcement has some symbolic value, this small step for an atheist is also a pretty small step for atheist-kind.