As yet, very cautious investigation of so, but not all of psychedelic agents in undergoing limited experimental testing. Some like LSD, have known possible side effects (insanity and unpredictable flashback at any later time) so bad that they would never pass an ethical review board and get funded.
As I understand it, the present experiments invoke using them in carefully selected patients, Once, in a very strictly controlled and monitored guided meditation. Some reports have been very positive for resolving issues such as depression.
They are still at the point of primary research, so anything verifiable would now be likely not yet published or deep, deep into one the very technical journals. Nevertheless, they have been mentioned on some news programs,
I would not say they are "slowly being accepted." More like "People are grudgingly giving way to the possibility that this might possibly be of hep to someone.
Meanwhile there are other, more promising areas of research - such as exploring ketamine therapy, that are much closer to gaining some acceptance into legitimate, non-experimental practice. They are alike in that they have the potential to get the depressed condition to just resolve, rather than remain a chronic condition under treatment.
In any case, just in case you or anyone reading is depressed, proceed to be evaluated be an appropriate health care professional. They are a long way from being deemed safe an effective. Professionals will give you treatment that is both,.