No offense, QC, but this post betrays a rather large lack of understanding about how these living history groups function.
I suggest that you look at some of WWII reenactor unit websites. It might be enlightening for you. It is the norm for these groups to pick a specific unit to recreate. That way, they can focus on keeping a consistent and accurate portrayal of a WWII combat unit. Can you imagine what it would look like if you had twenty members of a group show up for a battle and they each chose their own uniform ot wear? you would have a mish-mash of unifom types, insignia & ranks from all different periods & theatres. It would not be an accurate or effective portrayal of WWII combat. When a group decides to portray a specific unit, they are able to control such things. That is what keeps everyone from showing up dressed as a general.
This group is quite typical and these groups primarily exist to recreate battles & give educational public demonstations. Individuals within a group have their own reasons for joining that may include an appreciation for period military tactics, uniforms & equipment and culteral bits like period music, cooking and soldier's pastimes.
Here is a link to the governing association that their group is a member of. they also frown on actual nazis. Pertinent reading is in their by-laws & the "about us" section.
Regards, Canis