my impression was that using Bayesian-type approaches outside of purely statistical situations is a large part of what they are about.

Yes. I disagree.

Do you mean that it shouldn't be used to prefer one person's argument over another's?

Look at our good friend Scott Alexander dissecting arguments. How much actual B does he use? Usually just pointing out basic innumeracy is enough "oh you are off by a few orders of magnitude" (but that's not B, that's just being numerate, e.g. being able to add numbers, etc.)

Assuming you're both trying to approach the truth...

I think the kind of stuff folks in this community use to argue/update internally is all fine, but I don't think it's a formal B setup usually, just some hacks along the lines of "X has shown herself to be thoughtful and sensible in the past, and disagrees w/ me about Y, I should adjust my own beliefs."

This will not work with outsiders, since they generally play a different game than you. I think the dominating term in arguments is understanding social context in which the other side is operating, and learning how they use words. If B comes up at all, it's just easy bookkeeping on top of that hard stuff.

I don't understand what people here mean by "B." For example, using Bayes theorem isn't "B" because everyone who believes the chain rule of probabilities uses Bayes theorem (so hopefully everyone).