It's a misleading question. If it was just a game like MW2, then him being a Nazi doesn't make any difference whatsoever.
And don't argue with that, because Nazi doesn't mean Anti-Semite.
Agreed. For every German soldier that did not like Hitler, there were just as many who did. I can easily imagine someone in that time supporting nazi ideology, and believing that Hitler was doing good things for their country.
And the anti-semetism? Some points.
1) There were soldiers in the German army who were Jewish (but secretive about it).
2) Many Germans were in denial about the holocaust, or at least, willfully ignorant. As common as anti-semetism was many people would not accept the idea that Hitler was murdering Jews, assuming they were aware of anything going on at all.
3) The allied forces have gotten very sanctimonious about the whole Jewish situation. Anti-semetism was rife throughout Europe and (to a lesser extent) in the US. On hearing about the death camps, many British and French civilians were actually
pleased to hear that someone was killing off the Jews. Eugenics were still in their hayday, and it was only until after the war that such a degree of racism went into decline (mostly as a reaction to Germany's behaviour).
So yes, there is a huge scope for making a German character; the idea of being on the losing side, the idea of possibly feeling betrayed as the Russians close in, the pride before the fall when Germany took France and ousted the British, the witch hunts for Jews, the possibly conflicting ideals of whether one can be patriotic to Germany yet anti-nazi/Hitler (or vice versa, or both).
There is a huge scope for good story telling but (and this is a big but), is it too late for this kind of thing? There is so many damn WWII war games out now, we'd be bored of seeing the same period yet again, despite being from a new perspective.