The teaser trailer for “Maestro,” which Cooper directs and stars in, debuted Tuesday and offered the first close-up look at Cooper’s makeup and performance as the great American composer and longtime music director of the New York Philharmonic. Cooper, who is not Jewish, dons a prosthetic nose as part of his transformation into Bernstein, who was.

To some, Cooper’s nose in the trailer seemed like the kind of outsized caricature that has been a regular feature of Jewish portrayals throughout film history. The nonprofit group Stop Antisemitism called it “sickening.”

“Hollywood cast Bradley Cooper — a non-Jew — to play Jewish legend Leonard Bernstein and stuck a disgusting exaggerated ‘Jew nose’ on him,” the group tweeted on X.

Bernstein’s three children — Jamie, Alexander and Nina Bernstein — on Wednesday issued a statement supporting Cooper, saying they were “touched to the core to witness the depth of (Cooper’s) commitment, his loving embrace of our father’s music and the sheer open-hearted joy he brought to his exploration.”

“It breaks our hearts to see any misrepresentations or misunderstandings of his efforts,” the statement said. “It happens to be true that Leonard Bernstein had a nice, big nose. Bradley chose to use makeup to amplify his resemblance, and we’re perfectly fine with that. We’re also certain that our dad would have been fine with it as well.”

The Bernstein children added that “strident complaints about this issue strike us above all as disingenuous attempts to bring a successful person down a notch — a practice we observed perpetrated all too often on our father.”

A representative for Cooper declined to comment. Netflix, which is distributing the film, also wouldn’t comment.

“Maestro” is set to premiere next month at the Venice Film Festival. Netflix will release it in select theaters Nov. 22 and on the streaming platform on Dec. 20.

The Cooper-Bernstein situation is multilayered; it touches not only the issue of stereotyping but the larger question of casting when it comes to certain groups. In recent years, there has been much debate throughout the acting world over who can and should portray certain characters, particularly in an environment where some groups have struggled over the decades to get regular and substantive work in Hollywood.

Emma Stone was criticized over and apologized for playing a half-Asian character in Cameron Crowe’s 2015 film “Aloha.” Tom Hanks has said if “Philadelphia” (1993) was made today, it would star a gay actor, “and rightly so.” Some LGBTQ+ advocates have argued that trans roles like Jeffrey Tambor’s in “Transparent” and Eddie Redmayne’s in “The Danish Girl” ought to have been played by trans performers.

Those discussions have been largely focused on the authentic portrayals of ethnic minorities and LGBTQ+ characters, but some have argued the same perspective should also apply to Jewish characters. The stereotype of the large Jewish nose in particular has persisted in through centuries, from Shakespeare’s Shylock to Nazi propaganda. “While the hooked nose is but one antisemitic caricature of many, it is particularly pernicious in that it is assumed to be true,” writes the Media Diversity Institute.

“Jews Don’t Count” author David Baddiel earlier this year criticized the casting of Irish actor Cillian Murphy as Jewish physicist J. Robert Oppenheimer in Christopher Nolan’s “Oppenheimer,” along with the casting of Helen Mirren as former Israel Prime Minister Golda Meir in the upcoming film “Golda.”

“Casting directors are now frightened to cast except in line with the minority they are casting,” Baddiel told the Times. “But they are not so worried about Jews.”

Others have argued that transformation is an innate aspect of acting. Mark Harris, the Hollywood author and journalist, dismissed the controversy.

“We are not going to start fall movie season with a stupid ‘backlash’ controversy over an actor wearing makeup so that he can more closely resemble the historical figure he’s playing,” Harris wrote on X. “That is what actors have done for decades and will continue to do.”