My thoughts on the subject? I'm clear that while it's perfectly acceptable for Quakers to participate in/practice the sweat lodge, it is not acceptable for it to be considered a part of Quaker practice - it steps away from one of the most basic tenets of Quakerism: that we need nothing to mediate in our relationship with the divine.

As for the cultural appropriation side of things, I understand that in calling it a sweat and using the form it does, that there is at least some adaptation going on. But then I look at other cultures that use similar set-ups for religious or secular purposes and I can't help but think that the Quaker Sweat organizers have just as much right to practice that form of worship as the Native peoples do. Really, I don't have complete clearness on this side of things.

And this is the short version. If you want more detail than that, I can likely provide, but I don't have time right now.