Really? As a minority and member of other protected groups, I have had to endure what you characterize as "hate speech" many times and yet I remain in complete opposition to the goals of your movement. The restrictions on speech and thought championed by your movement are contrary to the ideals of classical liberalism and, in my opinion, are a hazard to the continuation of a free society.
Your movement does not speak for me and I wish nothing to do with them. I suspect that I am far from alone in this regard among minorities.
However it seems as though your idea of a free society doesn't extend freedom to people for whom hate speech is a much greater obstacle.
Does extending them freedom from one problem by removing a greater freedom from both them and the rest of us sound like a good bargain? It doesn't to me nor does it seem so, thankfully, to a great many others.
Why haven't they had to interface with it? Because they have privileged positions in society, so hate speech has never been directed at them. Their lives have never been made harder to live by someone else in an influential position saying they don't deserve to exist.