Coastal Mississippi, Coastal Alabama, Charleston and Savannah also had relatively large number of Catholics.
I don't think a Protestant government of the CSA confederation would be inclined to harass or suppress Catholics. Sure, there was some religious animosity from various preachers with small followings. Historically, however, the Confederate leadership identified with and respected the ancien regime aspect of the Catholic church as they felt it encouraged traditional social arrangements and traditional culture. Of course, "traditional" to the CSA meant "Planter Culture"
Most of that was hostility to immigrants (of whom a strong majority were also Catholic). Though there was a faction of the KKK inherently hostile to Catholics as a religion, most of the KKK divided Catholics into "indigenous" and "immigrant"- then saved the hostility for the immigrants- especially those with non anglo saxon appearances.
Well within an independent CSA, the concept of the second wave KKK, is likely a useless point. With slavery maintained, there would be little reason to have an organization focused on maintaining Southern pride or culture or what have you. The KKK was a result of a sense of loss felt by many European individuals and communities in the US south and then continued loss going into the second wave.
Agreed on the Catholic part.