I've never met a progressive who "denounced all argument" about immigration. Instead, they seem tired of the same handful of (xenophobic) tropes that get trotted out during national discussions around immigration policy: immigrants as social burdens, as criminals, as drug mules, as "anchors" for some dogwhistled demographic replacement, &c.
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...