I'm assuming you're thinking if slavery was kept in the CSA long term (which is pretty ASB, but let's go with it for the sake of the question)
Since many religions have a tendency to adapt to the society they're around, so you'd have the same pattern here. We've seen it in the US with large parts of the ELCA* shunning traditional Christian positions based on Scripture and the tradition of the Church Catholic (not = what is normally called "the catholic church") to be more "inclusive" and what have you, because "inclusive" is the buzzword of the day.
Thus, you'd have branches of the mainstream churches in the CSA developing theologies to justify slavery and racism, and then you'd have those called "fundies" rejecting those theologies as heterodox, at best.
* Only using them as an example. There are plenty of OTHER examples. And, as always, within the ELCA, there are the symbolic 7,000 who haven't bent their knees to Ba'al yet.