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.