I am not sure quite what you mean here.
All the school districts in the Raleigh/Durham/Chapel Hill area of N.C. are thoroughly integrated. But it is specifically the Durham system that is regarded as dominated by black culture, low achievement, discipline problems, hip-hop culture, etc. Many young professional people actively wish to support a diverse culture, in theory, but they have a look at the Durham school situation and want no part of it.
The Durham school board has been such a circus over the last couple of years that it has been written about in the WSJ. One of the members was a convicted shoplifter and completely representative of the worst of black urban culture. She is ignorant, loud, and filled with racial suspicion and animosity to which she gives full voice. If she is criticized, that is disrespecting the community, don't you know.
School board meetings repeatedly turned into shouting matches with her playing to the Jerry Springer segment of the Durham black community and them attending the meetings in the spirit of Jerry's audience.
The most ironic thing about the whole circus is that the white schoolboard members being condemned for their racist attitudes are very much liberal/progressive types.
Here in Nashville, amongst whites who can afford otherwise...only "crusaders" purposely send their kids to failing public schools for the diversity or to make a statement.
This is the state of public schools in nearly any metro district in the South.
Black families who can afford it suffer no such illusions and send their children to private schools like anyone with a brain would.