I take zero pleasure in saying this, but "the other side" is fucking insane. There's no arguing from first principles, let alone acknowledging that there are issues of concern with one's propositions.
In the case of "free speech", there's a failure to acknowledge the fundamental proposition of it when used in the US -- in that it's about the government not being able to prosecute you for speech that it doesn't like. This is literally the basis of the OP.
I'm a fan of Christopher Hitchens and he embodied that "free speech absolutism" argument convincingly (as otherwise its a pathway to censorship and oppression), but I think it's also important to recognize Karl Popper's Intolerance of Intolerance.
This stuff is no longer idle speculation -- it is an active facet of authoritarianism that is playing out around us right now.