I don't know the background conflict. But at least one of taw's points is correct. Any prior P, of any agent, has at least one of the following three properties:

1. It is not defined on all X -- i.e. P is agnostic about some things
2. It has P(X) < P(X and Y) for at least one pair X and Y -- i.e. P sometimes falls for the conjunction fallacy
3. It has P(X) = 1 for all mathematically provable statements X -- i.e. P is an oracle.

You aren't excused from having to pick one by rejecting frequentist theory.

To make use of a theory like probability one doesn't have to have completely secure foundations. But it's responsible to know what the foundational issues are. If you make a particularly dicey or weird application of probability theory, e.g. game theory with superintelligences, you should be prepared to explain (especially to yourself!) why you don't expect those foundational issues to interfere with your argument.

About taw's point in particular, I guess it's possible that von Neumann gave a completely satisfactory solution when he was a teenager, or whatever, and that I'm just showcasing my ignorance. (I would dearly like to hear about this solution!) Otherwise your comment reads like you're shooting the messenger.