Native reenactors walk a very fine line. This line is the one which separates historical interpretation from cultural appropriation.
We have become numb to the fact that the things we do affect other people. When it comes to living history, we are affecting a group of people of many cultures who were experiencing (and in some instances still do) an all out assault on their cultures for the past 400 years. It is more than understandable that Native Americans would be suspicious of a bunch of crazy white people who dress up as 18th century Indians on the weekend. It can certainly come across as cultural appropriation, espcially when those crazy white people refer to themselves as Cherokee, Mohawk, Lenape, &ct instead of as interpreting Cherokee, Mohawk, Lenape, &ct.
What is it that crosses the fine line? Well, building a sweat lodge at a reenactment for one. This is the interpretation of religion. That should raise all kinds of red flags. "But we can interpret a church survice on Sunday." Yeah, but that is part of YOUR CULTURE! The sweat lodge and all things surrounding it, have never been part of European culture. Sweating was not something done for an audience, and there was more to it than just hanging out in a sweat lodge.
Take a minute and think about how your actions will affect another person or group. Recognize that to many tourists, their encounter with a Native reenactor might be their only encounter with "an Indian" no matter what your actual blood quantum. It is imperative we recognize our place and responsibility.
In the end, please do not cross the barrier. The actions of one person can have ripples which will affect someone hundreds of miles away, years down the road. After 400 years of attempted cultural genocide, American Indians are still here. Cultural appropriation is just as vial as cultural genocide.