WASHINGTON—When Andi Kasarsky’s husband died six years ago, members of her synagogue came to sit shiva—the customary Jewish ritual of mourning—with her. They came in shifts for days, many of them strangers, to share her grief. And although Kasarsky was mourning her husband, many of the grievers were gay. She was so touched by the support that Kasarsky, 54, became a more faithful member of Bet Mishpachah, an unaffiliated Washington congregation of around 200 gays and lesbians. She’s just one of many heterosexuals who are finding God in predominantly gay houses of worship. “Mishpachah means family and they were truly...