There's plenty in OA that for sure doesn't jive with some current views on appropriation. It depends on who you ask whether something is offensive.
I don't think cultural appropriation is a blanket negative, as some folks believe. We're the melting pot of a country that we are because we've appropriated traditions from various cultures around the globe.
The problem with trying to be sensitive to appropriation is that to do it successfully, you'd pretty much have to remove OA from scouting entirely. Every element of it is technically "appropriation", the lore, the stories, the lessons, the ceremonies, the costumes, the objects, they're all "appropriated" from native american culture. And in removing the appropriation, you remove something that, although flawed, does still recognize a culture in a way that most of these kids wouldn't otherwise be exposed to at all.
So it's a question of: Is a display of appropriated culture better or worse than no display of that culture at all? I'm not sure what the answer is.
I think a good way for the OA to move towards a more respectful appropriation of native culture would be to tone it down on stuff that most of the boys don't understand the significance of. I made it as far as Brotherhood and I could never have explained most of what the costumes, face paint, and sacred objects meant. If OA is going to use cultural items, they could do a better job of explaining what they mean.