For years, Asuman Antepli, a nurse at a hospital in North Carolina , said people mostly just ignored the head-covering hijab she wears as a mark of her Muslim faith.

Occasionally, a patient might make an insulting comment, but she would put that down to ignorance. Once, after Osama bin Laden was killed in 2011, men in the street made obscene gestures and cursed at her as she drove home.

But in the past year, as Donald J. Trump began his dizzying political ascent, things got markedly worse for Ms. Antepli. Some patients, or their relatives, openly recoiled at the sight of her. Others wore Trump hats and T-shirts, as if to prove a point. A handful have flat-out refused to allow her to treat them, even though she worked in the emergency room.

“It’s been very painful,” said her husband, Abdullah Antepli, who teaches Islamic studies at Duke University and has heard similar accounts of casual discrimination from his students.