Yes.
Yes.
Hmmmm...just for the sake of argument, let's change that around:
Are we religious bigots if we refuse to vote for a believing Wahabbist Muslim?
A person's religious beliefs, especially if they are strongly held, are the foundation for their interaction with the world. Why then should we completely ignore the religious affiliation of a candidate when considering whether or not to vote for him/her?
Does this make us bigots? I suppose in some situations it can become bigotry. But for most Americans it is just one of many shrewd and thoughtful ways to judge between candidates.