Those sympathetic to Mr. Trump responded with chants of “Lock her up!” and “U.S.A.!”

Even tournament officials were absorbed in the mix of sports and politics. Derrick Cooper, a rules official from Warrington, England, said friends were amused when he told them of the course where he was scheduled to officiate.

“They all said, ‘That’s interesting — to say the least,’” Mr. Cooper said. “I don’t think I’ve ever refereed on a golf course that’s owned by a president, so it’s definitely a first.”

Those inside the gates felt detached from the clamor at the course’s doorstep. Cody Waring, 18, of Montgomery County, Md., came with his grandfather, both of them in “Make America Great Again” caps. Mr. Waring said he had canceled plans to attend the Washington Nationals game when he heard he might have a chance to see Mr. Trump at the tournament.

“I think it’s an important statement to make with the hat — you bet,” Mr. Waring said as he waited for a group to finish putting on the 15th hole, near a plaque featuring a questionable piece of Civil War history that Mr. Trump credits to the course.

“I just want to show support for the president,” Mr. Waring said. “I know he’s going through tough times now with the way the news media is covering him, in ways that I would call unfair.”

Brian Jamerson, of Williamsburg, Va., said he was not bothered by the president’s continued connections to the course. “His name was already here before he got elected, so I don’t think he’s put himself in any worse position than he was already in,” he said. “As long as he keeps his personal actions out of it and lets his son do more of the work.”

By day’s end, even the golf itself could not fully escape associations with Mr. Trump. The winner of the tournament, Bernhard Langer, was caught a few months ago in a presidential controversy of his own, when Mr. Trump told congressional Republicans that the “very famous” golfer had confirmed to him clear evidence of voter fraud that he had witnessed while waiting in line to vote in the November election. Mr. Langer, who is a German citizen, was, in fact, in no such line, because he is ineligible to vote.

“Please give my best regards to your dad,” Mr. Langer said to Eric Trump at the championship trophy ceremony.