The problem is that the social justice warrior outrage junkies have used the term "hate speech" so frequently that they have unwittingly diluted it to the point where it's pretty much synonymous with "everything my opponent says".
Calling people homophobes, bigots, Christo-fascists, racists makes them feel like they are hated.
And perhaps they are hated. But guess where that leads to?
Goose/gander, pot/kettle, tu quoque....etc.