The assassination of Caesar is part of the script of the play, which was written 418 years ago by William Shakespeare; the choice to depict the title character as akin to President Trump is part of a long history of productions of the play that have used the text to explore contemporary politics. In 2012, another American production of “Julius Caesar” depicted the title character as President Barack Obama.

The decision by the Public Theater, which oversees Shakespeare in the Park, to depict Caesar as Mr. Trump has prompted social media protests from conservatives, and two corporate sponsors of the theater program, Delta Air Lines and Bank of America, withdrew their support. A third sponsor, American Express, as well as the National Endowment for the Arts, took steps to make sure the public knew they had not supported the production.

Defenders of the Public Theater, saying the play does not sanction political violence but is instead a cautionary tale about the use of antidemocratic means to defend a democracy, have said the critics are misconstruing the play and this production.

Two critics of the production demonstrated outside the Delacorte on Friday night, while a slightly larger group of defenders held a counter-demonstration.