“Boycotting our brands only harms hard-working employees and their families and is counter to the positive progress that we should all be encouraging and delivering at a time when our nation seems so divided,” Marty Maloney, a spokesman, said.

Mr. Trump and his daughter have stepped away from executive roles at the Trump Organization, which still earns money from golf courses, hotels and other properties around the world. (Ms. Trump has also stepped away as head of her brand.) Because Mr. Trump’s company is privately held, it is hard to know what impact his presidency has had on his businesses. But the merchandise side of the Trump licensing empire may be more vulnerable to negative attention.

“Retailers around the country are going to say, do we need the aggravation or not,” said Wendy Liebmann, chief executive at WSL Strategic Retail, a consulting firm. “It’s hard to imagine that if a brand is really, really doing well, a retailer like a Nordstrom or Neiman Marcus would cut off their nose to spite their face.”

Rosemary K. Young, senior director of marketing for Ms. Trump’s brand, said in a statement that the company keep expanding and that it had “significant” year-over-year revenue growth in 2016.

Representatives for Macy’s, which sells Ms. Trump’s clothing, handbags and shoes, did not respond to requests for comment. The retailer dropped Mr. Trump’s clothing line early in his campaign after he called Mexican immigrants “killers” and “rapists.”

Companies have also faced pressure to back away from “The Apprentice” franchise, of which Mr. Trump is an executive producer. Kawasaki said last month that it would pull its sponsorship, though the Japanese company seemed to backtrack somewhat within hours.

Ms. Coulter said the Honest Company, whose products will appear in an episode of “The New Celebrity Apprentice,” had committed not to advertise for the rest of the season or next year. The brand confirmed that it had limited involvement with the show, which has not yet been renewed for 2018.