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 WWII, the Democrats were the conservative party in U.S. politics, and the Republicans the radicals. That the roles of the Civil War era remained intact in-universe isn't that improbable.
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.