So if you are trying to work out which hypothesis is simpler, how do you do that? You use your personal intuition.

I was using Solomonoff Induction as an example of a system that uses Occamian priors. My question was on those who assert that they don't use Occamian priors at all, or for that matter any other type of objective prior. This usually seems to lead either to rejecting Bayesian epistemology in general or to asserting that any arbitrary prior works. I actually have no problem (in theory) rejecting Bayesian epistemology, as long as you still use some sort of probability-based reasoning.

When I referred to "personal intuitions" I meant controversial or arbitrary-sounding personal intuitions, such as "I feel there's a god" or "I feel abortion is immoral" and then using those intuitions not as some sort of evidence but as priors. I get why someone would perhaps use universal intuitions as priors, along the lines of "there exists an external material world", but why use an intuition where you know the next person over likely has a different intuition?