Atheists are the most hated and distrusted minority in America. This is not a surprise.
This is a ridiculously false statement. Atheists might be the most disliked minority, but there's a huge difference between being disliked and just outright hated. I'd say muslims are probably the most hated.
If a state elects an Atheist Republican, it would be a liberal state like Minnesota or Massachusetts. If we're talking strictly Republican states electing an Atheist Republican, Alaska or maybe Montana would be a good guess.
Jesse Ventura was an atheist, correct? Someone in that mould would fit your model well.
I like to think that America has forgotten Jesse Ventura held elected political office. But yes, he is an atheist. At least he is now. He wasn't very open about it during his time served as Governor.