It bugs my bones that Americans associate separatism with white supremacist ideals and slavery.
Are you talking about modern day America, or that of the Civil War era? Civil War era separatism was motivated by white supremacy and slavery. Any modern day separatism is foolish in general, regardless of motivation.
I wholeheartedly believe that sooner rather than later this country will split into an increasing number of successor republics. I am certain that some of those, particularly the states that emerge in the Southeast, will be pretty much like apartheid states, even more so than the US is currently. However I would expect better of the states that arise in the North and the West.
No. We already fought a civil war to decide whether states could secede, and the Confederacy lost. Even if white supremacists want(ed) to secede their home states from the rest of the nation, they can’t.