ATL culture is always a fascinating thing to explore, but a lot of this thread does tend towards "planet of the hats"-style oversimplification. To immediately qualify my own statement: it does depend a lot on exactly how the CSA gains independence, and what territory it holds. A Deep-South-only CSA that gained its independence after a long and bitter struggle is going to be a different beast than a CSA that has all of the Upper South and won its independence (relatively) easily-- through foreign assistance, for instance. That first nation may well become a rabidly entrenched slavery-will-always-be-sacred pariah state with an explisively plantation-based economy, becoming ever more isolated as the world at large begins to impose embargo measures. But the second secenario is completely different. Abolishing slavery will still be difficult, but to such a nation, international pressure actually means something. We must assume that regardless of frosty relations with the USA, it would be as normal a member of the international community as similarly slave-owning Brazil. Only later on, when the pressure mounts to get rid of slavery, do tensions arise. But for such a nation, I see it ultimately being resolved in the 'put a sunset on slavery' way, rather than the 'hermit kingdom of horrors' way.
Needless to say, the "mess struggling to survive" and "culture like nazi Germany" notions apply only to the first scenario, and not at all to the second scenario. These two scenarios are, of course, what one might call the worst and best case scenarios, respectively. In reality, we might expect some situation in between the two. Yet a lot of people seem to think that the CSA will automatically become the worst case scenario, which is a bit strange, I believe. The idea that the CSA wouldn't last long enough to see film technology develop is equally strange. A nation, having won its independence, is not just going to fall apart again. Even in the 'worst case scenario', the embittered Deep South rump-CSA would understand that only by holding together could it ever hope to preserve its "way of life" (for which it had bled so much in its costly war of independence). The idea that the people of the CSA would be too backwards to comprehend how film technology works is just... patently absurd. The exportation of a hillbilly stereotype (which is hardly a real life portrayal in any case) to an entire nation.
So... given the premise of a CSA that neither suffers its worst case scenario nor enjoys its best case scenario, what might we expect of its eventual cinematic culture? Personally, I would expect the following:
-- Clear 'content codes' (i.e. censorship laws), but on a state level. Something may be permitted in one state, but not in another. This is hardly something I see the CSA instituting on a national level. (This is a country that, at its constitutional convention, seriously debated whether the central government should be allowed to build public infrastructure of any kind, and ultimately settled on restricting such works to the most essential sort only. That kind of mentality is not likely to see the central government get involved in film production...) More likely, large film production firms will institute their own voluntary productation codes, to ensure that major productions can be shown in all the states.
-- A certain obsession with patriotism and the Confederate war of independence. The USA in OTL is rather fond of such heroic historical films about the ARW (and the Civil War, for that matter). Considering the sheer amount of monuments and equestrian statues commemorating the Civil War in the OTL South, I think that such themes will feature prominently.
-- A distinct lack of films showing 'dangerous blacks' and such matters. On the contrary, films will go out of their way to show how eveything is in good order, and how everyone in his right mind - even the slaves - ultimately benefits from the way things are. If rebellious slaves are ever shown, they will be portrayed as inherently evil characters, trying to tempt the 'good' slaves to the 'evil' ways of dissent. Their 'malign' influence will only end up hurting the 'good' slaves, these 'villains' will always be 'exposed', and the loyal slaves will be shown to have been 'right' all along. In other words: expect propaganda, rather than fearmongering.
-- Considering that a good number of Indians fought on the CSA side, there may well be positive feelings regarding that. The 'loyal Indian sidekick' may become a stock character, portrayed essentially positively.
-- Most of all, I expect the CSA's films and television programmes to be essentially... normal. Regardless of certain censorships and cultural biases (both of which were quite present in the USA in OTL, incidentally), seeing Confederate films from the 30s or 40s will be quite a lot like seeing OTL US films from the same period. The difference may be less focus on stories set in big cities, and more of a romantisation of the genteel, upper class rural life.