[tel]

That's definitely an interesting space. I think the highly principled side of the Bayesian boat would state that meta-hypotheses are tied into your prior on model building information (Pr(I), etc) and that it needs to be updated alongside everything else. So now if your hypothesis' posterior becomes something like Pr(H, theta, I) the whole business needs to be updated and will include all the meta level intellectual rigor. At this point I feel like I might be walking into the space of Structural Causal Modeling and I'm not too well versed there at all.

In the informal setting though you're only ever likely to be trying to "update" one belief at a time, so, yeah, it definitely requires intellectual care to make sure to follow dependencies. Worse though, is that it should be possible to two have codependent estimations and if you aren't aware of that codependency you won't ever be able to get along.

I think that's all interesting, but I'm not sure it applies to informal situations as well as one might hope. Frequently, Bayesian techniques are only used informally in conjunction with strong rationalist heuristics which help to build these reductionist hierarchies of effects and then allow for clear(er) methodology to find an accurate answer.

Few people thinking carefully and rationally would be willing to bet on their beliefs so long as they know that thy have an outstanding miscalibration. That's why scientists, good scientists anyway, will so often preclude things with disclaimers. They want you to be aware of whatever biases they can before you start to judge their opinions.