Yes, the goal of the modern Civil Rights Movement has basically been to say "in these areas, even though Bayesian inference produces statistically valid results

Yes, the goal of the modern Civil Rights Movement has basically been to say "in these areas, even though Bayesian inference produces statistically valid results, we as a society have decided that it's immoral to use it." What axes are OK to use Bayesian inference on and what are not is a philosophical and historical question with lots of practical implications across politics, economics, actuarial science etc. It's really worth thinking about. But here's a start: in general, people are more forgiving of inferring data from mutable traits than immutable ones.