Nigeria, South Africa, and New Zealand et al have film industries. One of my favorite movies is Colombian and the Russians did a terrific job on Nightwatch. So I expect the Confederacy will have some sort of movie development if it survives into the 20th century. I also think the notion that Texas goes it's own way is much less likely as they get all the perks of internal markets without having to shoulder the whole of their own army/navy
Many countries do have film industries of their own not just the countries you had mentioned. Even some major Hollywood films over the years had all or some of their scenes filmed in New Zealand, Australia, Mexico, Canada.