But how strong is the effect? It's not just a binary judgement. People can heavily bias based on features that are borderline irrelevant. Also, you may end up hurting a lot of innocent people by generalizing too much based on some feature that is not causally associated with the actual crime, even if it predicts well overall.

Are you comfortable applying this same bayesian logic to other factors like race?

There are 2 separate issues. Firstly, are people correctly estimating their priors, or are their priors unfounded.

Secondly, and more importantly I think, what effects does a 'correct' bias have when it starts interacting with other people. It might be the optimal choice in isolation. But that doesn't make it a good idea game-theoretically if everyone starts doing it.

The end result can be difficult to explain though. Because it means that not taking certain useful information into account leads to better decisions.

I think that, sometimes, we argue that a systemic bias is stronger than the statistics warrant. When sometimes the argument should be that sysyemic bias, statistically warranted or not is harmful.

(Note, my original comment was me making the mistake I argue against in this post)

It doesn't matter,your opinions of them does not matter to justice. The facts of the case is all that matters for justice.