Fridge / C.S.A.: The Confederate States of America
Part of the reason for the documentary's strong negative light is the fact that it's made by theBritish Broadcasting Service, and the Brits aren't terribly fond of the CSA given their neutrality with Hitler during World War II. Of course, there's also the fact that the CSA's a slave-holding nation that treats minorities like chattel. The fact that the documentary's controversial in the CSA because of its viewpoint is touched upon in the introduction.
Kennedy as a Republican? Well, during the Civil War era and all the way up until The Great Depression, the Democrats were to the right on minority issues in U.S. politics, and the Republicans the more Liberal/left-leaning on that front. That the roles of the Civil War era remained intact in-universe isn't that improbable, nor the fact that the Northern Democrats (who on account of sympathies with the South advocated "peace" and opposed reconstruction) end up becoming Les Collaborateurs to the Confederates.
The Southern white supremecists weren't exactly fond of Irish Catholics, who were ironically, a base for the Northern Democrats. The Union Army recruited Irish Catholics fleeing the Potato Famine, granting immediate citizenship in exchange for their enlistment, and without Reconstruction, the Irish Catholic base might have shifted to the Republicans instead of being a solid one for the Democrats (generally a party for white immigrants).
Japan as an Allied power in WWII? Makes perfect sense considering that they were an Allied power in WWI and that an alliance between Germany and the CSA would make Japan superfluous to Hitler.
Hispanics are one of the very few, if not the only ethnic minority spared enslavement by the Confederacy, instead being subject to apartheid. While it might seem jarring that the ultra-racist, white supremacist, Confederacy would spare any minorities, it makes more sense when you realize that most Hispanics are either entirely white, or mixed European and Native American (another ethnic group implied to have been spared enslavement). Its likely that that the CSA view Latinos as "tainted" or "lesser" whites rather than as human livestock and therefore decided that they instead have to simply be segregated rather than enslaved.
It could also be a case of Pragmatic Villainy since Latin America is several times the size of the core CSA. Perhaps even the Confederates realize that governing an entire continent made of up of somewhat developed nations that are confirmed to have put up a decent fight against the CSA`s conquest would be a nightmare if they tried to outright enslave it's inhabitants.
How did Abraham Lincoln survive to the age of 97 to do a TV interview, complete with sound, in 1906, twenty years before such technology was invented? Well, he is in exile in Montreal, and the film indicates that, due to the serious brain drain from the CSA, Canada is rapidly advancing past the CSA technologically. So perhaps by that time, Canada has become advanced enough to develop sound film technology twenty years early, as well as the technology to keep a man alive to the age of 97.