I think that your comment would've been a lot stronger without the jab. Every time you call someone repugnant for having a particular bias (which we all do), you increase distance and decrease understanding.
Bigotry on the basis of religious grounds is repugnant wherever you see it, and should be called out wherever you see it, because it always results in atrocities. Casual bigotry like this only grows into collective hatred through complicity.
Reminds me of Christopher Hitchens's eerily prophetic view of the spreading of the word "Islamophobia" [0].
It does not. It only takes a bigot to assume it does, however.
Someone who makes even a rude assumption about a people isn't necessarily a bigot. They could just be wrong and you could correct them without insulting them in the same you would hope people would correct you if you said something inaccurate.
You might be pantywaiste about calling out bigotry online, but I'm not.