When he was growing up in a small Egyptian town outside Cairo, Omar began feeling sexually attracted to other men. Too afraid to talk to family or friends, he turned to Facebook for help, shielding his identity with a false name.

Scouring social media for information and advice is a common recourse for young men and women who think they may be gay and live in socially conservative Arab societies.

But it can lead them to therapists, spiritual leaders and influencers promising to “cure the affliction” of homosexuality through so-called conversion therapy, practices that aim to change a person’s sexual orientation or gender identity...