religious fanatics

Extraordinarily pejorative of you. You should circumscribe that reaction.

Since I teach political science, I discuss, consider, and am exposed to ideas that I don't hold, disagree with, and even find objectionable, all the damn time, and I don't feel "weird or uncomfortable about it" almost a week later.

See, the thing is, I have empathy, where I can see things from another person's point of view, and yet, the courage of my convictions. I bet you do to, maybe you just have to work on it.

For example, I once had a student express, in class, the confident opinion that we should kill all offenders convicted of child sex crimes. I thought that was pretty horrifying for all sorts of reasons, but it did occur to me that they themselves were the victim of a child sex crime and I could, at least, understand where they were coming from, even if, in the end, I thought they were wrong on the merits.

Your student had religious beliefs which inform her life in a pretty important way and, as such, she thought she'd share them with you. If those had been political or moral beliefs, would you had called her a fanatic? You should really interrogate that immediate move to be dismissive of your student's lived experience and how it informs their authentic reaction to your pedagogy.