On the other hand, practicing scientists consider Popper's falsification one of the great unifying themes guiding scientific research.
Though perhaps not as well-known, Popper's approach towards falsification of probabilistic claims is also a great read.
The way I read it, it really dates back to Hume and the problem of induction. Until we have a Final Theory to hand, we never really know anything. That is a statement of epistemology. But science can't proceed on that basis: people make decisions on where to focus their efforts, and not all hypotheses are equally worth considering. That is a statement of scientific pragmatism, and those two fields don't overlap as much as we'd like them to.
Feyerabend is easily read as continuing to conflate the two: "Hey, all knowledge is provisional, so you might as well study astrology." Maybe that's useful from an epistemological standpoint, but it's not helpful for grants committees to think that way. Nor is it helpful for epistemological anarchists to insist that grants committees never really know and therefore really should fund astrology. The question of how scientists actually work is an important one, but it's a separate question from what TRVTH actually is -- even though scientists would like to believe otherwise. They're not as close as they think.
It isn't helpful for anyone and we have very concrete examples of that to hand: Anti-vaxxers love to point out stuff like Vioxx, but never say a damn thing about all the drugs and therapies which are helpful, do much more good than harm, and which are "proven" to work for all practical intents and purposes. Being unwilling to attack stuff like anti-vaccine nonsense head-on because of some abstract epistemological nonsense kills people. There's no upside to that.
Saying "Nothing is absolutely certain, therefore it is absolutely certain that we know nothing" is bad enough. Actually believing it is dangerous in direct proportion to how much of a hand you have in shaping policy. The bus driver might believe in utter epistemological nihilism, but they'd better not veer into oncoming traffic just the same.
They get to be anarchic, as long as you can't prove otherwise -- and "prove" in the mathematical sense, not the scientific one. All it costs you is paper, pencils, and the price of a trash can. (Which they never use.) If you shut down the line of reasoning just because other people are incredibly, dangerously stupid, you're going to have to shut down pretty much everything.
Isn't this, along with and maybe encouraging p-hacking, a major cause of the non-reproducability crisis? Scientists hunting out supporting evidence instead of showing their theories don't easily break?
I'd say to the extent that this behavior contributes to the reproducibility crisis, it has more to do with not backing that exploration with rigorous experimentation.
But more to the point, I'd argue that the lack of funding and publish-or-perish atmosphere has more to do with it. Academics don't necessarily publish because the results are noteworthy, but because they have to, regardless of the robustness of their methodology.