I've taught at a private HBCU that was essentially open enrollment and at an open enrollment community college that was largely PWI but had students from many ethnicities. The HBCU was much more supportive for Black students (many of whom were the first students in their family to attend college) than was the community college. Both schools had faculty who were committed to promoting racial equality, and both schools had faculty who weren't especially committed. But the atmosphere and ethos of the HBCU were far more supportive. Unfortunately, the funding and endowment weren't.

It probably won't surprise you that the budgets for Savannah State and other Georgia state HBCUs (Fort Valley State, Albany State) were far lower than at PWI state schools. I haven't checked the figures recently, but I doubt they've changed much.

So you have a system that promotes equal opportunity but which is a subsystem within a larger system that does not. Such is the nature of American public education. K-12: good luck finding equal opportunity there. Private schools? Compare Fisk's or Morehouse's endowment with Harvard's. Contrary to what many on the right would claim, there is systemic racism in American education, and until it is remedied, there will be systemic racism in America.