In a tolerant society, one must be tolerant of everything except intolerance.There's an interesting self-referential element there that's reminiscient of Gödel's incompleteness theorems. To wit,
We can either have a system of rules that is consistent, but cannot account for all phenomena that are consistent with the rules, or have a system that is inconsistent.
In other words, the principle of tolerance in society cannot incorporate its own negation and still survive. One nuance here is that Popper doesn't necessarily advocate for restricting intolerant speech as much as speech that leads to incitement, which is somewhat in line with 1st Amendment protections in the US.
This reminds me of another situation where self-contradictory rule systems cause problems: gerrymandering.
The Supreme Court is soon to hear arguments in a case of partisan gerrymandering from Wisconsin. Roughly speaking, a partisan gerrymander (as opposed to a racial gerrymander) is one in which districts are drawn to favor a certain political party (the "partisan" aspect") as opposed to favoring a certain race.
While racial gerrymanders have been repeatedly struck down in court (the latest being a case from Texas), partisan gerrymanders have a much more mixed record, which is why many are watching this new case with great interest.
One potential argument in favor of allowing partisan gerrymandering is that if a party wins, their victory should allow them the power to redraw districts -- the "elections have consequences" principle. But it seems to me that this is again an example of Popper's paradox of tolerance.
That is to say, if we allow the party that wins an election to do partisan gerrymandering, then we are allowing through the democratic process an action that will serve to directly reduce the ability of the democractic process to represent the people. And for that reason a partisan gerrymander should not be allowed.
I wonder if there are other settings where this principle might help clarify the limits of a permissive rule structure.