The political philosophy of most of the upper class in the south was based on a vision of an agricultural based "squirocracy" where benevolent landowners had slaves tended the land, and a sprinkling of yeoman farmers or tenant (white) farmers. There was a significant movement that, after the war, property qualifications would be reintroduced for the franchise (as was true in the UK at that time still) so that only those "with public not private interest" would vote to prevent plebian democracy of self interest. The educational system in the south in 1860, and for a very long time after the war, was centered on education beyond basic literacy with private tutors or private (pay) schools to educate an upper crust and a limited number of universities (southern politicians fought hard against land grant schools before and after the war) and this was for whites, forget educating blacks.
On the religious side, Catholics were tolerated only in the pockets where they were a significant presence (think Louisiana), and Jews while not absent were a small minority. Given the preferences for any immigrants, both Catholics and Jews as well as Southern and Eastern Europeans are unlikely to end up in a CSA in significant numbers.
Would there still be slavery in the CSA in 2019, almost certainly not. Would there still be apartheid or a severe Jim Crow, almost certainly. Same sex marriage, legal abortion (the wealthy will always have clandestine access), readily available birth control for unmarried women, bikinis on Florida beaches - nope. Because of a long history of slavery (no matter whether it ends in 1900 or 1950), and the subsequent enforcement of apartheid/Jim Crow in the face of a sizable black minority and the more open USA along a long border (and radio and TV that leaks across), the CSA will of necessity have developed a strong police system backed by laws, which can suppress a gay pride movement as well as it can suppress a black movement against restrictions.