The parent isn't talking about paradigm/approach; they're talking about how a certain class of people ("statistics-users in or from academia", let's call them) tend to believe in things like the "statistical power" of an experiment, which—while only sensible under frequentism—isn't really a frequentist idea, but rather just a peculiar tradition of academic rigour from before it was easier to multiply large numbers in meta-analyses.

Or, to put that another way: by "frequentism", the parent poster is referring to those people who believe that one thousand experiments on five people each add up to nothing, because none of them individually had enough power to draw a significant result. And by "Bayesianism", the parent poster is referring to those people who just do the five-person experiments and use whatever data they spit out, however noisy it is, because fractions of a bit of information are still more information than they had before.