I am well aware that racism ran very, very deep at the time. For example, the federal minimum wage law was originally intended to get the South in line with other parts of the nation in terms of what it paid and it was a de facto attempt to outlaw the practice of paying blacks about half what whites got paid for the same work. It was passed prior to WWII. It was failing terribly. The initial result was that blacks got fired in droves (which is part of what drove blacks out of rural Southern states into big cities of the Northern states). They weren't able to make it stick at all until after WWII began.
So I know racism ran deep. It was open. It was intractable. And it was not, per se, the reason whites invented the suburbs and moved there. Unprecedented middle class wealth was the driving force behind the invention of the suburbs. Blacks tended to be left out because blacks were generally left out economically. They also would have been left out had well off whites invented some other housing solution. But leaving them out was not the raison d'etre for the invention of the suburbs.