The only time an actual precedent has been set and an actual court battle has been won was in the Utah State Supreme Court. The specific case is
STATE of Utah v. James W. MOONEY, aka James W.B.E. Mooney, Linda T. Mooney, and Oklevueha Earthwalks Native American Church of Utah, Inc. Dated June 22, 2004.
The court ruled that card carrying ONAC members in the state of Utah do have the right to cultivate, transport, and consume Lophophora williamsii for religious purposes if acting within the ONAC code of ethics regardless of whether they are federally recognized tribal members. There has never been a precedent set regarding ayahuasca, cannabis, or any other plant medicine specific to ONAC. The church does claim the right to use all plant based medicines and in practice, in Utah, small scale cannabis cases almost always get thrown out because of precedent. I know of no other cases involving other botanicals at this time.
The other precedents they claim, specifically the Religious Land Use and Institutionalized Persons Act of 2000, United States v. Boyll, May 10, 1990, and the UDV and Santo Daime rulings respectively to my knowledge have not actually been presented and ruled on in a courtroom with regards to ONAC membership.
Several other states allow for the religious use of peyote by people who are not members of a federally recognized tribe (I believe Colorado is one of these). However, this is independent of ONAC membership.
Just be aware that anywhere outside the state of Utah, and even in Utah any material other than L. williamsii, has no actual legal precedent. There have been several cannabis and other cases that have turned out unfavorably for ONAC members in other states.
I have personally sat in the tipi with ONAC leadership and I am satisfied with their intentions and supportive of their mission. Just be aware that when working outside the church's home state and with the various branches, the legal protections they claim to offer may not hold up when tested in a judicial setting.