This sounds like a classic example of one faculty member hating on another. Unfortunately, this happens quite often, and as a graduate student you will have to deal with it most of the time because you are seen as a confidant for all kinds of neurotic professors who are obsessed with trash talking and having somebody listen to their hate-speech. This is especially true of toxic departments where people have larger than life egos.
Just like in every walk of life though, there is a caveat to the above scenario. Example: My MA program was a pretty toxic place where faculty hated on each other quite openly. My advisor, being head and shoulders above the rest in every aspect imaginable, would often let me know about the tribalism going on in the department with his office door wide open. He'd never bag on anybody for their methodological orientation, but simply because they were, quite frankly, horrible mentors, advisors, and didn't really care about their students, teaching, or the department. I was fine with it most of the time because he saw me as a confidant and I really got the sense that his frustration emanated from caring deeply about his students and their future. So, what I'm trying to say here is that there will be times when a professor bags on someone for legitimate reasons. That's fine--you take it for what it is and let it go.
Unfortunately though, most of the time people talk smack about a faculty member who, for whatever reason, doesn't get off on the methodological fetishism of his/her peers. The debate goes from intellectual differences to personal attacks over who gets more funding, who has published more and all kinds of other crap. Once again, you as the graduate student will be the first person to hear about it because you typically spend a lot of time with you advisor.
My advice to you is to generally stay away from department politics as much as you can. People won't judge you for being neutral but they will certainly judge and hate on you for taking sides. And since reputation is everything in grad school, once you get on somebody's bandwagon, it will be incredibly hard to reverse the damage.
I don't think you're overreacting here. However, I would advise against changing advisors as this is something that is very common in academia--faculty have strong opinions and they're usually not afraid to express them. You can certainly change advisors later but for now, I would just keep my head down, do my work, and not buy into the politics and drama.
Grad school is all about improvising and learning on the go, and negotiating the advisor-advisee relationship is almost an art form.
