See the "Tolerance and freedom of speech" section in the Wikipedia link for further discussion of how the idea applies to speech.

I’ve read the Wikipedia page. I also own the copy of the book where it is mentioned, which I’ve also read. People are paying it way more attention than Popper himself did (it’s not even mentioned in the original text proper) and further treating it as some sort of immutable law, when that completely ignores the purposes for which the argument was created and that it was never a formal observation of how society actually operated.

Sometimes I like a remixed version of a song better than the original.

The paradox of tolerance is not some narrow tool, it can be used in many contexts. In particular, it can be used to demonstrate that, if you want to exist in a society that has a coherent notion of "self-defense" in general, you must admit the existence of the paradox and the necessity of judging actions in the context of aggression or defense. To wit: killing someone is against the law, but killing someone who's trying to kill you may be permitted, but even in that case, the aggressor still isn't allowed to kill you just because you tried to kill them in self-defense; they forfeit the right to self-defense by being the aggressor.

The difference is that speech, even unpopular, controversial, insulting, and dehumanizing speech, isn't violence. There is no legitimate claim to self-defense aside from direct threats to one's own life or property.

But we're not talking about speech, we're talking about tolerance. Speech is just the medium. And lack of tolerance is a threat to one's life and property: redlining housing developers in the US did not tolerate black people buying homes in white neighborhoods; Nazis do not tolerate Jews to live. Intolerance is not "just" speech, it is speech as a direct encitement to actions that are intended to have negative consequences for the targeted party.