As a rabbinic student in 1980s New York, Denise Eger lived away from other seminarians. She quietly started a group for fellow gay and lesbian students, but held the meetings in another borough. By the time of her ordination, she wasn’t formally out, but her sexuality was known, and no one would hire her. Later, she took the only job offered, with a synagogue formed expressly as a religious refuge for gays. Since then, the Reform Jewish movement—Eger’s spiritual home since childhood—has traveled a long road toward recognizing and embracing same-sex relationships. That journey has led this week to Philadelphia,...