This seems impossible. Due to our unfortunate history certain racial groups are disadvantaged socioeconomically in ways that will show up across most statistically relevant data.
It seems like the best you could achieve is a system that was not racist amongst a group of people with the same socioeconomic background.
I can see how "prove a negative" is an extremely unlikely bar for anyone to clear, but I can also see how there's a problem with just accepting that socioeconomic conditions created in large part through racial inequality isn't an excuse for bad outputs. I don't think it's necessarily a problem with AI systems though, as you say they're going to reflect reality, and that reality is biased through long periods of economic inequality.
Maybe the solution here is to focus more on the people using the AI system, and less on the system. If people use the outputs of the AI as a kind of fait accompli, then it becomes an excuse to perpetuate existing inequality. Maybe we shouldn't be tolerating people using the existence of ongoing inequality as an excuse to further widen the gap between haves and have nots.
Having said all of that, I have no idea how that would be implemented in practice.
It seems like the best you could achieve is a system that was not racist amongst a group of people with the same socioeconomic background.