I cannot say how much the German Jews thought of themselves as German.
One of the reasons the Jews were hated was the Jewish involvement in Communism in Central and Eastern Europe at the time. Jews often made up over 30% of the NKVD units in the USSR (http://www.ukar.org/shapov01.shtml). And it was NKVD units that committed most atrocities and mass murders of Christians. This is why the East Europeans welcomed the Germans as liberators. The Germans knew this and the East Europeans knew this. The American people didn't know it and most Americans still don't know it. The Nazi persecution of the Jews was a mystery to me until I learned of the role that Jews played in Communism.