A quick thing that can be easily dispelled: minority groups didn't voluntarily move anywhere from '34 to '68 [1], because the FHA policy of redlining prevented them from getting a mortgage in predominately white neighborhoods. Shockingly or not, the higher quality property was reserved for whites.
'68 was the end of formal, legal requirements to disapprove of mortgages in heterogeneous communities (for lack of a better term). There's plenty of evidence that the practice continues even to this day, informally. [2]