Nearly four-fifths of white evangelical voters plan to cast their ballots for Donald J. Trump despite his multiple marriages, lack of piety and inconsistency on the issues they care about most, a new poll has found.

Support for Mr. Trump among white evangelicals is even stronger than it was four years ago for Mitt Romney, the previous Republican nominee for president, according to the poll of religious voters, released on Tuesday by the Pew Research Center.

White evangelicals make up about one-fifth of all registered voters and are a coveted bloc who, when energized, can turn out the vote through their churches and social networks. It has been unclear to what extent Mr. Trump will be able to capture this core Republican constituency, because some leading evangelicals have spoken of being disturbed by his penchant for boasting about himself and belittling others, his pledges to deport Mexican immigrants and bar Muslims from entering the country, and his past support for abortion rights and gay rights.

Some influential evangelical leaders have joined the “Never Trump” camp, while others have pledged support for Mr. Trump. More came on board after he wooed about 1,000 of them in a closed-door meeting in New York.