What do you base this on? I agree with the points you make but disagree that white parents do not want to see more black and brown teachers. When I first moved to my current West Coast home I was shocked by how segregated this city was and is. However the public school my kids attended, which was the best in the city and in a wealthy area, had black and asian teachers and none of the parents had an issue with this fact. In fact parents fought to get their kids into some of these teachers classes.
My problem with these parents is they could not see the message they sent to their kids when they or their kids treated their housekeepers and gardeners poorly. Given the segregation of the city this might be the only contact with blacks or hispanic people their kids had, and the parents were sending a message to their kids that these people were “less” or not deserving of basic respect. Of course these parents were the first to ask me if I was glad to have left the Midwest which in their minds was filled with bigots or people who married their siblings. In their minds they were good liberals.