Linguistic puzzle

Here is something that has popped up in my mind many times over the years. I am a fan of linguistics. Words matter, as does punctuation. (this ties in with some of the positions that I have put forth many times on this site.

Terms for various forms of hate/discrimination:

Racist – a person who discriminates based on race

Misogynist – one who is prejudiced against women

Sexist – one who discriminates based on sex

Agist – a person who discriminated based on age

Ableist – a person that discriminates based on physical ability or lack there of

Now, what about hate/discrimination for all, some, or one faith?

I have not been able to find a term in the English language for this situation. The nearest that I have been able to find is Antisemitism. The problem there is that it is hate for just those of the Jewish faith.

Yes, you could use a very lengthy list of terms for a person with hate against those of various faiths; bigot, asshole, prick, thoughtless, discriminatory, and the list goes on.

As one who enjoys language, I would to either learn the proper term, or coin one for it.

With root words and suffixes in mind, theist came to mind but that word is already taken.

Theist – One who believes in the existence of God or gods.

Antitheism is not too far off but that is the opposition of faiths.

What word would you suggest?