In a Washington restaurant on Monday, a woman with a toddler approached Scott Pruitt, the administrator of the Environmental Protection Agency, and told him to resign over his policies and his repeated spending scandals. Kirstjen Nielsen, the homeland security secretary, was interrupted at a Mexican restaurant last month as protesters chanted during her meal. Employees at a Virginia restaurant urged the owner to ask Sarah Huckabee Sanders, the White House press secretary, to leave in response to Trump administration policies, including the deeply unpopular practice of separating migrant children from their parents at the border.

Now the debate has reached far beyond the capital, to a place that has long been both an escape for the wealthy and an open forum for intellectual debate, where figures like Valerie Jarrett, Vernon Jordan and Carly Simon can be spotted playing golf, chatting at a cocktail party, or picking up local vegetables at a farm stand. On the Vineyard, Mr. Dershowitz is one of the most outspoken defenders of Mr. Trump, in a place frequented for decades by Kennedys, Clintons, Obamas and other Democratic royalty.

“It’s rare that I meet a real Trump supporter among the summer crowd,” said Tony Horwitz, a Pulitzer Prize-winning author and year-round resident of the Vineyard.

Mr. Dershowitz is not the first high-profile figure on this island whose views have been met with disapproval: In 1972, an artist was reported to have tried to throw Robert S. McNamara, the defense secretary who was an architect of the Vietnam War, overboard from the ferry to Martha’s Vineyard.

In a phone interview from his Chilmark home, Mr. Dershowitz said that he has not supported Mr. Trump’s political agenda, but has merely defended the president’s civil liberties, as he would for any person. Mr. Dershowitz said that a Vineyard friend who is a professor at the Massachusetts Institute of Technology had led an email campaign against him; he declined to name the professor.

“There’s a whole cabal of people who have decided that they will try to get people to stop interacting with me,” Mr. Dershowitz said. “The campaign has utterly failed. It’s affected my life zero. I’m not looking for sympathy.”

But he said that something had shifted on the island over the years, that opposing viewpoints were less welcome. “Anybody who wants to debate me, fine,” Mr. Dershowitz said, suggesting that he might set up chairs for debate at the Chilmark Community Center and invite anyone to attend.