Bear with me here :P

In its naive form, i.e. "In light of recalcitrant evidence, a theory is falsified and therefore must be revised or discarded completely", I think falsificationism is quite dogmatic, it doesn't take into account auxiliary hypotheses (e.g. the instruments failed or were not calibrated, background effects, there were implicit assumptions in the experiment that were not considered in the theory, etc.). I don't think any scientist takes this form of falsificationism seriously.

Ever since Kuhn and Lakatos (among others) came around, history of science was introduced into philosophy of science to improve our depiction of the scientific enterprise. It turns out that the kind of critical rationalism Popper hoped to see doesn't model how we do science at all. How so?

Humans and our degrees of belief happen to vary a lot more. Having experienced academia, I would say this is the case. The sigma threshold for a discovery in different fields of physics differ. The use of Bayesian statistical analysis also differs. The absolute "strength" of a justification of a method, theory or model is often judged arbitrarily, even though we do have good intuition on relative strengths between different methods of theory-justification. On another note, theories on rationality using statistics work better and are less controversial than falsificationism.

Perhaps it is an ought/is problem. Popper said we ought to be critical rationalists. But most scientists aren't. So maybe he still has a point. But does it matter? We still make the same predictions at the end of the day. Science isn't maths, science is vastly more social than maths. It's better modelled with ideas that scientists work in groups called paradigms or research programmes; we have some dogmatic beliefs about our theories, we often let politics influence it, or influence politics ourselves. One might want to uphold strong critical rationalist princples, but might find themself deviating from it once they join a PhD programme where they adopt the "culture" there.

So no, I don't think it's a tenable position. I think it's noble what Popper tried to formulate, but it was quite conservative; on the other hand, his contemporaries made important revisions and adjustments to it and their positions are more appealing in my opinion.