“Social conservatives need to maximize turnout from the base and expand the map by stressing the softer side of the faith agenda: education reform, immigration and criminal justice reform, and anti-poverty measures,” said Ralph Reed, founder of the Faith and Freedom Coalition, which has extensive outreach to conservative evangelicals in battlegrounds across the country.

“This will help with suburban women, millennials and minorities,” he said.

That approach, if followed, would be a stark departure from the issues social conservatives have championed since they wed themselves to Mr. Trump as a candidate. The Republicans’ white, religiously conservative base has motivated its troops for Mr. Trump around opposition to abortion rights, a conservative majority on the Supreme Court and support for Israel.