I wouldn't ever vote for an "atheist." I don't care if a person believes or does not believe in God, but no politician should wear their beliefs on their sleeves. It's about making a country work, not saving souls.
That said, I have voted Republican and consider myself fairly conservative, although in an economic not a social sense. More libertarian than anything really, but definitely not aligned with Democrats by any means.
I'd even venture to say that MOST Republicans do not care about religion. It's just a small minority of conservative Christians who demand it. But those people wouldn't vote Democrat and they live in the traditionally conservative south anyway, so I don't know why politicians pander to these people. Also, I'm a Christian.
Anyway, if a person doesn't wear their religion, atheist or otherwise, on their sleeve then I'm all for them as long as their policies are good.