In all likelihood, we'll end up with a Deep South that is heavily polarized along racial lines (monolithically Democratic blacks and monolithically Republican whites) with Republicans having a lock on all major offices; and an Upper South that is equally Republican, with token Democratic presence in cities. The Democrats will do their best in the South's border states (Virginia, North Carolina, Florida and Texas).
This will basically be a mirror image of the situation a century ago. (From Reconstsruction up until the '60s, the only Southern states that had any Republicans in Congress were Virginia, NC, Texas, Florida and Tennessee).
That's what we have now. But in the future we will have a monolithically interior south while the South Atlantic states (VA, NC, SC, GA and FL) will be swingy. They'll still be pretty racially polarized but there will be enough minorities and liberal whites in the fast growing urban areas to make this region competitive. So the new divide in the south will be east vs west, instead of upper vs lower.