Unfortunately I don't think we'll come up with a simple set of universally applicable rules and move on.
I do know that my abuse-free internet experience is very much a bubble, and every time I have been given the opportunity to see the experience of a "woman with an opinion" online I get to realize this. So let's as a society say "this isn't acceptable" and then deal with the much more difficult question of "what to do about it".
In any other commercial venue if a patron started shouting racist and sexist epithets, we would be ok with the owner throwing them out. We don't get caught up in slippery slope fallacies.
I can't scientifically prove that Fat-people Hate was objectively abusive but that's the beauty of social norms, I can say "I think it's abusive" and put pressure on businesses to remove its platform. Which is what I'm doing :)