Well that's when the genre evolves and characters shift from being brave former members of the Massachusetts 54th hunting down war criminals to Confederate deserters tracking down their junta supporting former commanders for revenge.
Then as time goes on, the genre will continue to evolve alongside America's conception of the south and the south's conception of itself.
Pretty much this. I could see Southers and Westers being seen as highly related genres - both deal with similar themes, such as the taming of a region and the constant threat of violence. But, obviously, there would be important differences as well: Southerns would deal more with the legacy of slavery and rebellion, and westerns would be seen as far more optimistic. But despite that, there would be a lot of crossover and the two would be n constant communication with one another.
I kinda suspect that Westerns would reman the more popular of the two, until the 20th century - but from there (especially as enough time has passed where people could look back and see how things developed) the Southern could rise to greater prominence.
I wonder how many legends of gunslingers will be produced in the South during this era. Its a lawless land, and outlaws, vigilantes and the like are going to be very prominent indeed. And more than a few of them are likely going to be targeting the planters and their remnants - there's a fair chance we get a few who could inspire Robin Hood-style legends.