The problem with banning "hate speech" is that the term is subjective. AFAIK, US laws already make it illegal to encourage violent behavior against anyone. So there should be no need for further censorship as far as public safety is concerned. In the end, these buzzword terms of "hate speech" and "bigotry" will be used as political tools. You can see how it's done already by watching cancel culture - 20 year old social media postings being dug up and interpreted in the least charitable manner possible, with the people doing the interpreting not even bothering to pretend they are actually concerned with anything other than the endorphin rush they get from "calling them out". It's a power trip. Now imagine this, but with actual power involved. That's what makes the left more dangerous than the right, currently.

This might've been different in the past, but right now it's obvious who the anti-science people are, and currently they control science along with the media as well. Women who are still more afraid of the right are delusional, no amount of misogyny makes a difference if there's no power to exert it. The real misogynists and sociopaths have long since switched sides. To them it makes no difference what kind of ideological BS to spew, they only care about the social rewards they get from spewing it.