There is simply no way to know the answer to this question.
First of all, we do not have polling data that could tell us what the average German believed during either of these wars. It certainly looks as if they tended to believe strongly in their national community, but people sometimes act outwardly in ways that do not correspond do their true beliefs. Without accurate polling, we can't know what they truly felt.
Second, it would be very difficult to know the difference between people who "really believe" and those who are "brainwashed." A marxist, for example, would argue that we in the US are brainwashed into thinking that we are free and have equality even though we "really believe" that we are.
To take just one example of how difficult this is, two historians have both looked at the same set of interrogations of Nazis who participated in the Holocaust. Christopher Browning argued that the evidence showed the men were motivated by peer pressure and a desire to advance their careers. Daniel Goldhagen's Hitler's Willing Executioners holds that the men were motivated by anti-Semitism.
Goldhagen would probably argue that the men truly believed in the national community, even when it led them to commit mass murder while Browning would say that they did not truly believe. We can never really know who is right.