While learning about the second world war during middle school and high school, there was never a time where we actually defined the solid differences between the German military groups in terms of ideologies. So, I, as well as many of the people around me, have grown up always referring to the German military simply as Nazis, instead of the German army.
From what I have learned while doing some independent research on this topic, that it is misleading to call the Wehrmacht as such. If I am not mistaken, the Wehrmacht was not involved in the implementation of the Holocaust, and that not all of the soldiers agreed with Nazism, but that they were fighting on behalf of Germany itself as the armed forces of Nazi Germany (not to mention the fact that military service was compulsory, so a majority was forced to fight). While it was just the SS that were really "Nazi Soldiers", as they were responsible for the implementation of the Holocaust.
What you have stumbled onto in your research is what historians call "the clean Wehrmacht myth." The idea that Germans were apolitical patriots was one that was cultivated after defeat and nurtured by various far-right groups. I would advise you to examine /u/commiespaceinvader 's answer to the question "Just how much of the Wehrmacht was dirty?" The linked answer pretty much the standard historiographic consensus these days on the Wehrmacht's involvement with Hitler and the ideology of the NSDAP.