Why does it matter to you how strong the correlation between race and culture is?

I don't care about the correlation between race and culture in and of itself. I want to remove or reduce (preferably remove) the percieved correlation between race and academic performance; and it seems to me that the best way to do this is to remove the correlation between race and culture (as the correlation from culture to academic performance does not look removable).

Isn't the real problem that people are mishandling Bayesian updates based on race? That could be solved by teaching people how to perform Bayesian updates more accurately. It wouldn't be a world in which "race doesn't matter," but it would be a world in which the extent to which race does matter is recognized and not exaggerated or ignored.

That is a good strategy, and quite possibly superior to my suggestion. The biggest trouble is that it requires a substantial majority of people to be willing to learn how to properly perform Bayesian updates, which I fear may make it less practical. (Not that my idea was necessarily all that practical to begin with).

I can think of at least two other causal paths from race to academic performance. One is the attitudes a person's peer group is likely to hold towards academic performance (even if they don't make a point of affiliating with other people based on race, other people may make a point of affiliating with them based on race), and more generally how the people around a person treat them based on race.

Hmmm. This is a possible path; intuitively, I'd expect it to matter about as much as the neighbourhood one grows up in. That is, I would expect any non-cultural effects to be more or less random noise.

The other is genetics. (I imagine this is not a particularly popular thing to say but I recently realized that I do not have a solid statistical foundation for dismissing it.)

That is also possible. Intuitively (which is very poor evidence, I know) I would expect this to matter less than culture. I do know some very intelligent people of many races; so individual variance seems large enough to defeat any systemic genetic bias that may exist.

Experimental evidence of the effects of culture versus genetics could be discovered by studying people of one race raised in the culture of another race (e.g. by adoption).