The Martha’s Vineyard Film Festival began on Thursday night with a premiere of the film Chappaquiddick. Two screenings were held at Edgartown Cinemas to sold-out audiences.

The twin screenings started half an hour apart so that director John Curran, writers Taylor Allen and Andrew Logan and star Jason Clarke could take part in question-and-answer sessions with both audience groups afterward.

But instead of asking questions, some viewers had statements to make about how they felt the film represents Massachusetts Sen. Edward M. (Ted) Kennedy (played by Jason Clarke), who caused the death of Mary Jo Kopechne when he abandoned her in his sunken Oldsmobile after driving off the Dike Bridge on Chappaquiddick in July, 1969.

“I want to thank you guys very much for portraying him exactly the way he was and portraying the lying coward that he was. Many of us know that,” said Woody Williams, who grew up in Edgartown and was preparing to join the Marines when the crash occurred. His words drew a smattering of applause and some nervous laughter.

Another audience member rose to his feet and pointed accusingly at the filmmakers, loudly charging them with a “very soft portrayal” of Senator Kennedy and invoking the name of Donald Trump before walking out of the theatre amid a hubbub of groans.

At the second screening, Chilmark seasonal resident and Harvard Law School professor Richard Lazarus also raised a comparison to the current president, but in a milder tone.

While acknowledging that he is “dumbfounded” at the way Mr. Trump’s supporters disregard his “obvious flaws and fundamental indecency,” Mr. Lazarus said, “It’s not a bad reminder for many of us that we are also willing to put a blind eye to someone’s flaws because of our political beliefs.”

“I was 15 years old on Martha’s Vineyard when this happened. People knew he committed homicide,” Mr. Lazarus continued. “He should have gone to jail.”

The film follows a brisk crisis-management cleanup quarterbacked by Robert McNamara (Clancy Brown), who at one point mutters “Bay of Pigs was a better-run operation,” as the headstrong Senator Kennedy rejects the advice of a room full of senior political operatives.

Strings are pulled in Edgartown, where officials are eager to minimize their senator’s predicament. Ms. Kopechne’s body is embalmed and returned to her parents before an autopsy can reveal she suffocated in the sunken car, which is agonizingly depicted in the film.

A court date is moved up and Senator Kennedy pleads guilty to leaving the scene of an accident, receiving a suspended two-month sentence. At the end of the film, he makes a television speech asking his constituents whether they still have confidence in him. As the end title informs us, they did, and he served in the Senate for the rest of his life.

Both screenwriters and the director said they were pleased that audiences had differing opinions about Senator Kennedy’s character in the film.

“I think Jason did a great job of embodying that, because it is so complex and there are so many questions,” Mr. Curran said.

“We weren’t interested in conspiracies, we were interested first and foremost in the truth," Mr. Allen said. "I think the truth has no political party and I think that’s something that applies today as well,” he added, to enthusiastic applause.

But, Mr. Curran said, the only two people who knew what actually happened that night were Ms. Kopechne and Senator Kennedy, and both are dead.

Audience members also had many questions about technical aspects of the film.

Mr. Clarke, an Australian actor known for Zero Dark Thirty, said he wore prosthetic teeth, worked intensively with a leading dialogue coach and listened to recorded speeches in order to master a convincing Massachusetts accent.

The filmmakers spent only a couple of days in Edgartown with a minimal crew, Mr. Curran said, to shoot exteriors and the Chappy Ferry.

“We didn’t know if we’d be welcome,” the director said. “We didn’t want to assume we would be... We didn’t want to create a bad feeling.”

The scenes involving the crash and the sunken Oldsmobile were filmed in Mexico, where the crew built a meticulous reproduction of the 1969 Dike Bridge and used the same water tank director James Cameron employed for Titanic.

But the bulk of the movie, Mr. Curran said, was filmed on the North Shore of Boston. Island audiences should be prepared to see a courthouse made of stone blocks instead of bricks, and other unfamiliar versions of Edgartown landmarks.

Chappaquiddick enters wide release April 6. It is rated PG-13 for “thematic material, disturbing images, some strong language, and historical smoking.”

The film festival continues at the Chilmark Community Center campus through Sunday evening. For a list of remaining movies and events, visit tmvff.org.