it isn't that you aren't allowed to have the spiritual practice, you are welcome to use mescaline (the active ingredient in peyote, which can be synthesized) however you want. It is also available in some other cactuses that aren't near extinct.

The intent of the restriction is to keep the harvesting of the peyote plant at a level that hopefully prevents it from going extinct. If everyone was permitted to harvest peyote, it would be available to no one at all very quickly. Native Americans get the exception because the tribal groups that use the plant have a culture of respecting it and being caretakers of it.