It is true (I might even call it a truism) that some people go too far and overreact, but I think it's important to step back and think for a minute about just how short a time it's been since these things were considered widely acceptable. Then think about how that affected the people still around today who had to sit through that. Then remember that, as I said, there are still many people today who are actively advocating for a return to that blatant bigotry.
This is why you get people who overreact even to genuinely-benign questioning of such policies: because it's very hard, in many cases, to tell the difference between someone who's just asking questions, and someone who's "just asking questions"[0].
Both sides can play this nonsense game. Not every perceived slight is bigotry or -ism. Stating the fact that men cannot get pregnant isn't transphobic. Stating the fact that Black people per capita are more likely to be both the perpetrators and victims of violence isn't racist. The immediate push back to even broaching these subjects, facts, and findings is what got us here. We're not even capable of discussing anything because any deviation from the party line is immediately perceived as the worst of the "opposition". If you state you're pro-free speech, you're a fascist neo-Nazi. If you're pro-trans children you're a pedo child groomer. Nuance and the capability to talk across the aisle has sadly disappeared, and everyone just gaslights and projects about the other side being sexist, racist, anti-White, Europhobic, Islamophopic, antisemitic, etc.