Based on David M's answer and the given examples:
Racism is ... the belief that your own race is superior.
Sexism is ... the belief that your gender is superior.
Nationalism is ... the belief that your nation is superior to others.
In their extreme form the above are commonly perceived as hatred, because the "believers" tend to "defend their superiority" against what they see as "subversive attacks" of whom they believe to be "inferior".
So I mostly agree with David M and I'd just written a comment, if I could (I can't because of low rep). What I wanted to add is that I'd propose "fanatism" as an equivalent to the provided examples:
Fanatism is the belief that your (often but not necessarily religious) belief is superior.
So, if you're looking for an "-ism" and are satisfied with "hate" and "religion" being implied only by common use, here you go.
Since I still lack the rep, I'm answering the comments here:
@Alfe: Strictly speaking you're right. But there are implications by "common use" that make me tend to agree with David's answer. And one of the implications is that one believes oneself to be superior. A black racist slave in the 19th century's Texas is just not significant in today's associations that come to mind, if you hear the word "racism".
@jwenting: The key note here is "In their extreme form...". "Defending" in the extreme form is attacking the "inferiors" who started the "subversive attacks" with more aggression. Although it might not be violence but only an aggressive tone or constant antipathy. This is seen as "reasonable" by the extreme racists/sexists/nationalists/...ists. The targeted persons (and some outsiders) will perceive this aggression not as defensive but as an attack on its own. Thus they will call it "hatred" instead of "reason".
In short: You're right.
Defending the belief ... isn't necessarily born out of hatred. It's the other way round: Hatred is perceived by those who you attack when defending your belief.
A nice example is the patriot's slogan:
"Who's not with us, stands against us."
I hope you see the aggressive undertone in the above statement. Btw. if you want to be picky, George W. Bush junior kind of declared war on Germany with these words in the context of 3rd Iraq war. After all, German chancelor Schröder seems to have been eavesdropped on subsequently. My favorite "equal pay" answer to this kind of provocation is:
"Patriot is another word for idiot, as you just made me stand against you."
Or to put it less blantly and thus deescalate things:
"No, thank you, I will not stop thinking on my own."
I picked up a lot of "perceived" "implications" and so. The question explicitly listed the "-ism"s and their implication of "hatred". So I think fanatism is a nice word to fit the list.
I just reread the question and noticed it's not "religious hatred" but "hatred against one/multiple religions" that's sought for. Fanatism in one religion often goes with the implied hatred for other religions.
@fredsbend: The one-word requirement is rather harsh on this one. You will either lose quite some accuracy or have people not understand the exotic term you got.