I'm from California, I never knew that bigot was specifically related to religion at all. On hearing the word I think first of race, pretty much synonymous to racist, but I would accept it being used for religion and gender, and I don't think I've heard it used much for things like political opinions. I certainly wouldn't say you could use it just for someone with an opposing opinion to you, or someone who strongly holds their opinion. A bigot not only strongly holds their own opinion and refuses to listen to other ones, a bigot also feels that people that don't agree (or aren't of the right race, religion, etc) are inferior, stupid, worthless, or something of that sort. Someone who refuses to listen isn't a bigot, only someone who also hates or feels superior to others. It's a pretty strong word.

As for other words, I have often felt the lack of a religion based word such as racist or sexist, and I have personally invented the word religionist, which has totally failed to catch on and I'm the only person who uses it.

And to go off topic a bit, I also feel there is a total lack of two necessary words, singular third person pronoun with no gender, (he or she) so that you don't have to specify. People tend to use they, but since that's plural it doesn't really work. It annoys me. And the other one is a word for a boyfriend or girlfriend. A husband or wife is a spouse, and brother or sister is a sibling, whats a boyfriend or girlfriend? Unlike religionist, there isn't any obvious way of contructing words for those two meanings, and I haven't run across any foreign languages that have them to borrow from.