It's very easy to let that slip into post hoc justification of your priors.

In my view, "prior" may be a misnomer. There is nothing that I'm aware of in Bayes' theorem to suggest that you have to formulate your priors before gathering or analyzing your data. I would describe priors as constraints that are included in an analysis, to narrow the results based on additional information that you're aware of. Bayes' theorem mainly provides a framework for computing what happens when you do that.

Maybe the prior doesn’t need to be formulated _before_ getting the data, but it needs to be _independent_ of the data.