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I pointed this out years ago: there are basically two natural philosophies when it comes to avoiding bias: either it's sufficient to (e.g.) mask race as an explicit input, or it's necessary to ensure the predictions treat all races identically. If you're against both forms but keep talking about how a system isn't "fair", you need to take a long look at what, exactly, you mean by "fairness".
Also this goes well beyond machine learning -- policing, insurance, etc. A lot of political issues aren't even at the point where productive discussion is possible, because nobody is willing to state unequivocally what they mean by "fair".
"Unfortunately" for the machine learning case, they lack the complex internal self-censorship that humans can do to be able to pull that off. Even if you mask out inconvenient inputs like race and gender the model will likely immediately notice clusters of correlated traits that stem from that, and reconstruct the race and gender from scratch.
(A fun idea for a dystopian story element: people conspicuously purchasing items and visits places associated with a "safe" demographic like elderly Asian women, to keep the eye-of-sauron AI off their backs.)
I'm not sure I really believe "self censoring" is a coherent concept. For example, if you're predicting the probability somebody will default on a loan and white people have lower credit scores than asians people, is any model that notices assigns asians a lower probability (on average) not "self censoring"? If 99% of people who eat sushi default on their loans, is it "unfair" to penalize them?
To be frank, I've never heard a definition of "ignores race" that isn't implicitly asking for just nakedly pretending all races have equal odds of defaulting on loans, regardless of whether that's accurate or not. I think people are actually asking for this "post-hoc fairness" should be explicit about that. Instead when I say "so you're saying we should just retroactively make the outputs of the result less accurate and pretend men and women are equally likely to commit murder", the response I get is "you're just straw-manning me, I just want a model that's fair".
It's frustrating that the complaints about bias seem contradictory and/or unsatisfiable, and the people making them are unwilling or unable to elaborate. If somebody is going to criticize my model, they should give me a well-defined notion of fairness that it's actually possible for my model to meet. If their definition of fairness means "deliberately cripple your model and force banks to give out loans that are unprofitable" they need to actually own that instead of hiding behind ambiguity.
Edit: The "post hoc" solution (which I think is the only solution that meaningfully satisfies progressive demands) is:
train a model that uses every variable
train a model that only uses variables you want to ignore (race, sex, etc.)
your predictions are model1(x) - model2(x)
Apparently actual progressives disagree, but I've never heard anyone give an alternative.
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