I would imagine after a generation or two. I'm sure even the most racist people realized that it was impossible to re-enslave the freedmen.
As for segregation, I would argue that in some southern states (not all) a majority of whites still is in favor of it.
I don't know if a majority in any state would say, even in a confidential poll, that they support segregation in public schools enforced by law, but I wouldn't be surprised if a healthy majority strongly opposed efforts at promoting additional integration.
