WYSIWYG has understated the situation by calling it complex.

Public school choice plans did much to weaken the public school system. An unintentional result was the growth of many charter and faith-based schools, leading to new kinds of segregation.

The growth of charter and faith-based schools owe much to the old ruling. In some areas, fewer children attend public schools than the 'pay' schools, and public money is going to the pay schools on the basis of numbers of students. A number of cities, including New Orleans, have more 'other' than public school students. Separate boys and girls schools are becoming popular again.

The result is that, with fewer students and less money, public school programs are much diminished.

Calgary in (Ha, ha) prejudice-free Canada now has Muslim, Jewish, charter, and Christian-religion-based schools of all stripes receiving their shares of the tax money, based on number of students in each school. Catholic ('separate') and public ('other') schools in Canada have long separated Catholic and Protestant students but now the latter are being separated as well.
Of course, here in Calgary the well-to-do and those looking for the best schooling for their kids for some time have had two or three private schools with restricted admissions. Some students are sent down east.

Small towns and rural areas have always had their segregated separate and public schools, but are much less affected by the other divisions of the cities.

An interesting situation has developed in Atlanta where there are now wealthy gated African-American in addition to white communities, and the charter (called something else in the States but I can't think of it) schools are performing the function of keeping children with their proper peers.

I don't know the answer, but to me, it seems that kids are being separated from each other, as they always have, by the drive of their parents to keep them with their own kind. The 'real' segregation.

The old ruling had only re-inforced that bent.