Edit: apparently I’m 20 minutes late and 4 other people said the same stuff. Oh well.

I think there is more going on than just “it’s ours, you shouldn’t have it” though. Peyote in the US is designated legal for religious use by indigenous people as part of traditional practices only. It’s also extremely slow growing and requires very careful harvesting to keep the plant alive, it’s listed as an endangered species in the wild, explicitly due to over-harvesting.

Basically people using it as a recreational drug can have a very real impact on the legality and availability of the plant for indigenous people.

The people in the OP are not engaging with any of this stuff and treating it simply as culture war, with an attitude of extreme contempt and hostility to the people who they see as potentially stopping them from getting high, which I find pretty gross - regardless of whether you think it’s fair to gatekeep the plant.