Karl Popper is not talking about today's progressives, because he died in 1994. The closest extension we can reasonably draw does not include them either, because Popper exclusively identified totalitarian ideologies with reactionary beliefs[1].
It's very easy to use the PoT as a blunt weapon, and there are some embarrassing applications of it on the political left. But none are quite as embarrassing as suggesting that Popper might seriously entertain "free debate" with a Nazi.
I didn’t say Popper would entertain free debate with a Nazi. My point is that, under Popper’s framework, there’s a huge incentive to declare anyone you don’t like to be Nazis, and reframe speech as tantamount to threats to physical safety.
Those tropes (and the reactionary politics that underlie them) strike me as precisely the kind of intolerance that Popper might have concerned himself with.
(Separately: it's unclear how progressives have satisfied the "intolerance of intolerance" condition here. Are you claiming that progressives have successfully won some on that front of the culture war? Current policy suggests otherwise[1].)
[1]: https://www.cbsnews.com/news/immigration-biden-first-year-ti...
(This really is a genuine question) who is to be allowed to determine if our opponents are that, and hence worthy of what one might call preemptive intolerance?
Dealing more abstractly: I personally think we are justified in practicing "preemptive intolerance" when the party in question (1) has a bad faith (not merely faithless) relationship with the "language" of our political systems, and (2) demonstrates repeated intent to employ the mechanisms of our systems to subvert them. Both conditions are necessary; the absence of the latter makes the individual a LARPer.