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.
This is the root of the problem with censoring "hate speech". I used to like the idea that we could punish people who make hateful comments, but if a hateful comment includes opposing viewpoints to relevant political viewpoints and anything having to do with "privilege", especially when "privilege" involves aspects about yourself that you have no control over, than this sort of thing really rears its ugly head as a war on free speech. Freedom of speech includes unpopular opinions.