Some forms of shamanism might,but they're not really organised religions are they?.Of course the Rastas view marijuana as a sacrament.That's all I can think of.Maybe there aren't really any because most psychedelics just blow religion out of the water.I mean in the Christian/Judaeo/Islamist sense.The only "religion" that has been able to hold water for me is Buddhism,which I don't see as incompatible with the psychedelic experience,although that said I haven't taken any psychedelics for a long time.Official Buddhist doctrine may hold psychedelics to be anathema,but I don't think they would be at odds with its cosmology,which includes "exchange of selves."
Santo Daime use Ayahuasca Native American Church use Peyote Bwiti use Ibogaine Temple of the True Inner Light Use DPT
Many tribes will use psychedelics in their ritual, but they won't refer to them as psychedelics, nor they are organised religions.
Many of the tribal religions are hybrids which are comprised of traditional beliefs and sometimes influenced by more widespread religions like Christianity, Catholicism, etc which is why the religious title is synonymous with the tribal names. Its fair to refer to them as religions, almost seems to come off as prejudiced and deragatory not to, as they are organized in their spiritual beliefs. Furthermore, Some of them like Native American Church have even been recognized as legitimate and allowed to practice under the Religious Freedom Act in the US for example. Perhaps because many of these religions have tradition of being passed down orally and they haven't sought the widespread missionary conversion of the more renowned religions in the West, the cultural bias makes it more difficult for some to recognize them as religions. The Psychedelics are often used sacramentally and ceremonially, often in rite of passage experiences and much like wine in Christianity, is often supposed to be a direct part of the people's God(s) , I have heard mushrooms referred to as Flesh of God for instance or the Psychedelics are viewed as gifts from God(s).
there are probably several sects of several beliefs that don't directly oppose doing so. and some traditions that involve the use of them directly, in the context of ritual. but there is nothing a chemical substance can do for the mind, that the mind cannot be trained to do for itself, using its own internally generated chemistry.