The paradox is used as an argumentative device for judging whether a tolerant and democratic society is possible (with liberal institutions ensuring intolerance doesn’t emerge) or if maintenance of tolerance would require an autocratic philosopher-king.
The continual application of it to the online censorship debate makes little sense in light of its original rhetorical context. It is also constantly cited in policy prescription proposals of which I would be shocked if Popper agreed with.
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.
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: men did not tolerate women receiving an education so that they could have a career; 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.
The one thing a tolerant society can NOT tolerate is intolerance itself. If allowed to set root, intolerance will take over and destroy the tolerant society. The intolerant will be loud and aggressive, working to silence everyone else. Eventually, it's over.
Just like the fact that people who want to live self-determining lives in a self-governing democracy must be always better armed and prepared than the bullies and autocrats who want to freely plunder and run other lives & societies. If they are not better armed & prepared (either personally or by proxy of police, military, etc.), then the bullies & autocrats will inevitably take over by force at any opportune time.
(See also in economics: The bad money drives out the good, every time.)
With any good faith effort, intolerance is pretty easy to define.
But, if you are talking in bad faith, there's 1000 arguments.
All authority is not authoritarian. That is why democracy was invented. In order to provide a self-correcting system. But yes, Churchill was right when he said that "Democracy is the worst of all forms of government, except for all others that have been tried."
Total free-for-all has repeatedly been shown to rapidly devolve in every case. Can you show a single un-moderated forum that survives over time, or a single unregulated "free" society without authority that does not fail?
So, can you show one of these no-authority forums or societies, or do you have a better suggestion than to just give up?
The continual application of it to the online censorship debate makes little sense in light of its original rhetorical context. It is also constantly cited in policy prescription proposals of which I would be shocked if Popper agreed with.