Religion does play a role for me, but not so much what they call themselves, but what principles they stand by. For example, I am a Catholic through and through, but I would vote for Mitt Romney or Mike Huckabee waaaaaaay before I would vote for John Kerry or a Ted Kennedy. I would love to see some Catholics in politics who stand for strong Catholic principles, like Alan Keyes, but those are few and far between. So I will vote for those who best support the Catholic principles that I believe in, and obviously right now it looks as if many non-Catholic politicians have those principles that the Catholic (by name) politicians reject.
As for voting for an atheist, that would really bother me, but it would have to go back to the principles the candidates I had to choose from. If it meant voting for an atheist who is pro-life vs a Catholic who goes against the Church and supports abortion, then I would vote for the atheist, and same goes for a Muslem. Those Catholics who intentionally go against the Catholic Church scare me way more than most other people from any religion. I have absolutely no respect for them.