The fundamental confusion going on here comes from peculiar terminology.

jsteinhardt writes:

Also, I should note that for the sake of simplicity I’ve labeled everything that is non-Bayesian as a “frequentist” method

So every algorithm that isn't obviously Bayesian is labeled Frequentist, while in fact what we have are two epistemological frameworks, and a zillion and one algorithms that we throw at data that don't neatly fit into either framework.