I don't have a problem in theory with banning hate speech, the problem is who defines what is and isn't hate speech. Denying the Holocaust, obviously hate speech. Saying slavery was good, also hate speech. Is being pro-life hate speech against women though? I've heard that said many times recently. I've heard people on this forum say that opposing affirmative action is hate speech. Is questioning the economic impact of immigration hate speech? It's hard enough to draw a line in the first place, but it's especially hard in the current culture where people are trying to outdo each other in terms of being the most "privilege conscious" person in the room. It basically becomes a competition to see who can label the most speech as hateful.
I wouldn't consider denying the Holocaust hate speech. Just stupidity that may come from a hateful place but isn't inherently hateful. To me, hate speech might be saying the Holocaust was a good thing/didn't go far enough/something the Jews deserved/etc. that can't be construed as anything but hateful. Same with slavery, which is hardly something only blacks/Africans have endured historically. Saying slavery is good, eh, not inherently hateful; saying blacks should be enslaved, etc., then yeah.