Well, for starters there is a massive ideological difference in the form of government. The CSA was all about getting the government out of your life (as long as you are white). The Nazis were all about getting as much government in everyones lives as possible (which was designed to be good if you were white and bad if you were not). Idk if southern people, as a southerner, would have liked totalitarian regimes no matter their view on race. Also, more than likely, slavery would have been banned at some point in a modern CSA (potentially as soon as 1900) with the advent of the cotton gin. It is not impossible to imagine that even if the CSA were racist (it surely would be) that they would not go as far as condoning mass genocide (particularly by the 1940's). Lastly, if the CSA were lucky enough to win the civil war, why would they risk that triumph by going back to ward at the behest of a European government? Particularly when none of the fractured German states nor Italy helped them out when they needed it? More likely, the CSA would have remained a neutral party.