As a Southerner myself, here's my take on the matter. I'm defining the "South" as the former Confederate states and territories (Virginia, Tennessee, The Carolinas, Georgia, Mississippi, Alabama, Louisiana, Arkansas, Texas, and Arizona), plus Kentucky.
I deliberately left out West Virginia in this analysis, because it was a major swing state for the longest time before becoming a Republican stronghold during the Obama and Trump years. Also, West Virginia is kind of a geographic and cultural anomaly in which region it belongs to. West Virginia was a loyal Union stronghold during the Civil War (which is how it achieved statehood) and is more "Appalachian" than generic "Southern".
Depending on who you ask, West Virginia is either the northernmost Southern state or the southernmost Northern state.
Of the states that make up the Old South, I'd say either Virginia or Florida will turn solid blue.
Both are already major swing states now but were former ironclad red states.
Virginia in particular is noteworthy for being one of the only Southern states that Hillary Clinton won in 2016 and is also trying to distance itself from being a "Southern" state and trying to re-identify as a "Mid-Atlantic" state. As a Virginian (I know, TMI) I have been witnessing the transformation of the political landscape in my state. When I was a kid, Virginia was solidly Republican, and by the time I graduated high school, it was a wild card swing state.
This "Mid-Atlantic" swing state mentality is especially true of the Northern Virginia suburbs near Washington DC, as well as Richmond, Charlottesville, and the coastal Tidewater cities (Norfolk, Newport News, Virginia Beach, etc.), although you even see similar sentiments in the centrist areas like Roanoke and the New River Valley college towns.
Granted, there are still some staunchly conservative areas of Virginia such as the Coalfields (the counties of Wise, Dickenson, Russell, Buchanan, and Tazewell), the Virginia side of the Tri-Cities (Abingdon, Gate City, etc.) and especially Lynchburg, home of Jerry Falwell and Liberty University.
There are also a few areas of Virginia that are the most "swing state" of all with an overall centrist political climate. The Roanoke Valley area is probably the most noticeable of these areas, although from what U have observed the Staunton/Waynesboro is fairly centrist as well.
Give it ten years and Virginia will be a blue state with Lynchburg as the only major Republican stronghold (sort of an inverse of Texas, a solidly red state with Austin as a left-wing stronghold)
Texas is kind of iffy, because while Austin is practically the Portland of the South and you have a very high concentration of Latinos, I get the feeling that most of the Latinos who would actively and regularly vote are more in line with conservative or centrist platforms, especially since Texas doesn't have Sanctuary Cities and unlike California, has strict voter ID laws making it harder for undocumented immigrants to vote (notably, this tactic has helped the Democrats control rural California).
Most Latinos tend to be devout Catholics and are ideologically more in line with the GOP compared to the liberal Democrats, especially the newer "Justice Democrats", but largely vote Democrat due to fear-mongering tactics from both parties regarding immigration. Tellingly, a lot of legal immigrants and third-generation and fourth-generation Latino Americans don't like illegals, the sentiment is stronger outside of the major coastal cities.
If it weren't for the uproar regarding ICE and Trump's wall, I'd say most of the Latinos in Texas that can legally vote, would probably go Republican, especially older Latinos (Boomers and Gen X'ers) and they're more likely to vote on a consistent basis anyway, especially in state and local elections.
Tennessee and Georgia do have a chance of going blue, but not before Virginia and Florida. Once those two states go full blue, then I could definitely see Tennessee and Georgia becoming major swing states similar to how Florida and Virginia are now.
North Carolina and Kentucky will probably remain Republican, although I could see specific cities and large towns becoming more "purple"
I don't know enough about Arkansas or Arizona to comment, in all honesty.
The least likely candidates to go blue would be Mississippi, Alabama, Louisiana, and South Carolina