For example, when Yvain speaks of philosophical Bayesianism, he means something extremely modest...

Yes, it is my understanding that epistemologists usually call the set of ideas Yvain is referring to "probabilism" and indeed, it is far more vague and modest than what they call Bayesianism (which is more vague and modest still than the subjectively-objective Bayesianism that is affirmed often around these parts.).

If frequentism and Bayesianism are just two ways of defining a word, then there's no substantive disagreement between them. Likewise, if they're just two different ways of doing statistics, then it's not clear that any philosophical disagreement is at work; I might not do Bayesian statistics because I lack skill with R, or because I've never heard about it, or because it's not the norm in my department.

BTW, I think this is precisely what Carnap was on about with his distinction between probability-1 and probability-2, neither of which did he think we should adopt to the exclusion of the other.