I'm saying that what they did was nazi shit, in alignment with nazi values, towards nazi goals, so I feel good about calling them nazis. Regardless of whether they would have called themselves nazis.
Why do you care so much about party membership? Why the project of establishing a high barrier and technical definition for what a nazi is?
My question to that would be: is a pacifist in the trenches of Vietnam on the side of the Americans equally culpable as the infantry soldier with a rifle? Both carryout essential tasks, both are likely conscripts. The only different is 1 has a rifle and didn't object to compulsory service. The other one made an objection but still performs an essential service.
I'm not trying to establish a generalizable moral calculus of culpability though. Just refuting the idea that soldiers fighting for nazi germany were somehow not nazis if they weren't registered party members.