For years, as the principal public voice for the Southern Baptist Convention, the country's biggest evangelical group, Richard Land warned of a "radical homosexual agenda" and pushed for a federal ban on same-sex marriage.

His successor, Russell Moore, sounded a different note when the Supreme Court in June struck down the federal Defense of Marriage Act. "Love your gay and lesbian neighbors," Mr. Moore wrote in a flier, "How Should Your Church Respond," sent to the convention's estimated 45,000...