People are not making the claim that nobody is right, so labelling it "relativism" is inappropriate. Merely pointing out that these norms are applied to everyone, and cut both ways. if somebody else thinks your views are odious and you ought to be silenced, what principled reason do you have for saying you ought not to be? you can take the route of saying that in fact your own views are not odious so you shouldn't be silenced, but your opponents are and therefore should be. But in that case all you've done is engendered a situation where every side feels comfortable and justified in attempting to silence their opponents. Because obviously, every side thinks they're right and their opponents are terrible people (note that I'm still not claiming that neither side is right). Discourse quality is degraded. And people start looking around for the next rhetorical nuke to throw at their percieved enemies. it's a race to the bottom, and the bottom contains mainly shouting, hatred, and fearmongering.

Norms like "people shouldn't be silenced even if their speech is despicable" are the Geneva convention in the war of the words. They're social technologies which allow people who disagree to coexist peacefully. These are the insights of the enlightenment, and liberalism as the word originally meant.