Where do you think priors come from?

Technically, the priors are the sum of the previously available information relevant to the topic.

you can always recompute all your priors from scratch

No, I can't. I'm human. What you are saying is theoretically possible in the sense that a full AIXI machine is theoretically possible, but I fail to see any relevance to real life.

Clearly in social justice theory, you're not allowed to use priors

On the contrary, you are expected to use very strong priors, it's just that they have to be particular priors and derive not necessarily from previous information but rather from what you ought to believe. I haven't noticed SJ being particularly interested in evidence.