They don't have a right to the chemical structure of mescaline though. It's like saying Chinese tea growers have the right to bar western people from drinking energy drinks because they both contain caffeine.

My dude, what? We're talking about settlers appropriating the culture of indigenous Americans. I'm not versed in the history of the Chinese Tea trade, but it has historically been exported and shared. The key difference being "Exported and Shared". Willfully sharing parts of your culture with other people is not at all comparable to having it be appropriated by colonizers despite your express protests.

Would you stop taking Aspirin if Egyptian people said that you were appropriating their use of willow bark?

Willow trees grow worldwide, and people generally use the resources that are available to them. There is definitely a case to be made about the imperialist nature of western medicine, but that is a completely separate conversation from what we're talking about here.

They have a right to the rituals, images, and other unique elements of culture involving peyote. They do not have a right to the chemical structure itself.

Why are you so intent on determining what parts of their culture they have a right to and which parts they don't?