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 churches. “They aren’t part of an evil conspiracy.” Marriage, he added, was a bond between a man and a woman, but shouldn’t be seen as a “‘culture war’ political issue.”

Since the birth of the Christian-conservative political movement in the late 1970s, no evangelical group has delivered more punch in America’s culture wars than the Southern Baptist Convention and its nearly 16 million members. The country’s largest Protestant denomination pushed to end abortion, open up prayer in public schools and boycott Walt Disney Co. over films deemed antifamily. Its ranks included many of the biggest names on the Christian right, including Pat Robertson and Jerry Falwell.

Today, after more than three decades of activism, many in the religious right are stepping back from the front lines. Mr. Moore, a 42-year-old political independent and theologian who heads the convention’s Ethics and Religious Liberty Commission, says it is time to tone down the rhetoric and pull back from the political fray, given what he calls a “visceral recoil” among younger evangelicals to the culture wars.

“We are involved in the political process, but we must always be wary of being co-opted by it,” Mr. Moore said in an interview in his Washington office, a short walk from Congress. “Christianity thrives when it is clearest about what distinguishes it from the outside culture.”

Along with much of the religious right, Southern Baptists are undergoing a generational shift as Mr. Moore and his allies recalibrate their methods and aims. The moment is significant not only for America’s religious life but for its politics, given the three-decade engagement by evangelical leaders that kept social issues on the front burner and helped Republicans win national elections.

Self-described evangelicals still vote heavily Republican. Exit polls show that nearly eight in 10 sided with Mitt Romney in the 2012 presidential election, a larger share of that group than either of the previous two Republican nominees received.

But Republican operatives with ties to the evangelical movement say much is changing. Every year tens of thousands of evangelicals, particularly the young, leave the Southern Baptist and other big denominational churches for more loosely organized assemblies that oppose abortion but are less likely to hew to other Republican causes.

“Republicans are finding it increasingly hard to collar evangelicals for political purposes, simply because the movement is so fragmented now, so decentralized, and a growing number of evangelicals simply find politics distasteful,” says Mark DeMoss,  a former chief of staff to Mr. Falwell and an adviser last year to Mr. Romney’s campaign.

Mr. Moore is responding to this drift. He warns evangelicals to avoid becoming “mascots for any political faction.” He focuses on how to keep millennials engaged in the church. His advice to church leaders: Be “winsome, kind and empathetic.”

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