World War II had a different story in Harry Potter, and it's a bit clearer in MoR. It was sparked by Grindlewald's desire to have dominion over the muggles - the muggle war was just a reflection of the wizarding war going on at the same time. Grindlewald was the real power in Germany, and Hitler just a pawn. The reason Dumbledore couldn't take down Grindlewald until the war was over, was that Hitler was fueling Grindlewald's power using dark rituals involving the blood sacrifice of millions of muggles.