Trump’s Opponents Want to Name His Big Donors. His Supporters Say It’s Harassment.

So far, he said, there is little evidence that the backlash against donors crosses that line. For Mr. Herricks, the Trump donor in San Antonio, his donation of $15,000 to the Trump Victory Fund, a joint fund-raising committee led by the Republican National Committee, and his $2,800 check to Mr. Trump’s campaign, have put him in the public arena, whether he likes it or not.

Economic boycotts are protected by the First Amendment, legal scholars said.

“If we see that people whose donations are highlighted publicly are being harassed, that’s a reason to be concerned,” Mr. Hasen said. “If the concern is someone will have a nasty tweet sent to them because of them being named by Castro, well, welcome to the real world.”

Others supporting an overhaul of the campaign finance system said it was more worrisome. “I’m not sure Mr. Castro’s simply throwing out the names of people with no ties to specific policy issues is helpful in this day and age of social media,” said Fred Wertheimer, the founder and president of Democracy 21.

For some Trump donors, the scrutiny has only made them more determined to support the president.

“The more they do this stuff, the more it’s going to backfire,” said Bill White, a former president of the Intrepid Sea, Air & Space Museum in New York. “More people are putting out their chests, standing up straight, saying: ‘I’m in. To hell with you publicizing my name.’”

Mr. White said he was planning to attend one of the Hamptons fund-raisers on Friday: a $2,800-per-person Trump Victory event planned for Friday at a Bridgehampton mansion owned by the real estate developer Joe Farrell. For people wishing to attend a V.I.P. reception and take a photo with the president the cost is $35,000, according to an invitation viewed by The New York Times.

Among the hosts of that event are Ronna McDaniel, the chairwoman of the Republican National Committee, and Donald Trump Jr., the president’s son, and his girlfriend, the campaign adviser Kimberly Guilfoyle. Jared Kushner, the president’s son-in-law and senior adviser, is also expected to attend.