They walked to the sanctuary in the frozen silence before dawn, footsteps crunching over the snow. Soon, hundreds joined in line. It was January 2016, and the unlikely Republican front-runner, Donald J. Trump, had come to town.

He was the boastful, thrice-married, foul-mouthed star of “The Apprentice.” They were one of the most conservative Christian communities in the nation, with 19 churches in a town of about 7,500 people.