I fully support integrated churches, but to my knowledge there are no laws keeping blacks and whites from worshiping together.
Only issue is folks have different worship styles. How do they propose overcoming that reality?
(Oh, in my former lily white PCA church we had a black deacon. He was a former black panther whose former life goal was to kill white people.)
My southern baptist church is the epitome of a conservative SBC and we have blacks and whites in our congregation. The whites out number the blacks but there is no conflict, it is what it is. The population of my small town is skewed to more whites than blacks. Our little church has vacation bible school each summer and the local black church always brings a bus full of kids and vice-verse if they have a vbs.
All this sounds like more PC hand wringing for something that occurred 100 or 200 yrs. ago. God leads people to where they attend church not political correctness.