Here's another perspective: since we have de facto segregation in most schools, White parents are more likely to feel that their (i.e. largely White) schools are going to be relatively safe to reopen, while Black parents are almost certainly going to feel that given the inequity already present in public schools, their schools are not likely to be adequately prepared.

Here's what a COVID-19 policy looks like at a truly exclusive (and expensive) private school:

https://www.andover.edu/2020plan

And here's a statement of their Community Health and Wellness policy:

https://www.andover.edu/2020plan/health-wellness