The big names who sit atop organizations that function largely as lobbying groups and mobilization squads for the Republican Party have stuck with Mr. Trump despite the lewd comments he made in a 2005 recording, even though he was never their preferred candidate. He wooed them and convinced them that he would appoint Supreme Court justices in the mold of Antonin Scalia, the conservative who died in February. To these pragmatic players, the election boiled down to only two issues, both that could be solved with Supreme Court appointments: stopping abortion and ensuring legal protections for religious conservatives who object to same-sex marriage.

But the evangelicals now challenging the old guard tend to have a broader agenda. They see it as a Christian imperative to care for immigrants and refugees, the poor, the environment and victims of sex trafficking and sexual abuse. Many support criminal justice reform and the aims of the Black Lives Matter movement. While ardently opposed to abortion, some are inclined to be more accepting of same-sex marriage.

“The next generation of evangelicals craves a less partisan, less divisive and more racially inclusive expression of political engagement that addresses concern on a range of issues, not just abortion and gay marriage,” said Jonathan Merritt, a young evangelical who writes on politics and culture.