The first time Stephanie Brinkerhoff tried psilocybin, she was a Mormon mother of three and desperate for help. She was struggling with migraines and chronic fatigue, and the antidepressants she had been on for years weren’t working, she felt. After listening to a series of podcasts about psychedelics, and learning about their reported mental health benefits, she presented her research to her Bishop, who didn’t dissuade her.

“He was just kind of like, ‘Ok, like, I trust you,’” says Brinkerhoff, who looks a lot like Sally Draper from Mad Men,...