Initially, it looked like a Hollywood coup: Zoe Saldana, a high-profile star, will play the jazz singer Nina Simone in the biopic “Nina.” And although Saldana isn’t known as a singer, neither was Reese Witherspoon before she won an Oscar playing June Carter Cash.

The backlash began immediately. A petition at Change.org, launched in 2012, objected to a “light complexioned” actress (Saldana’s mother is Dominican; her late father Puerto Rican) from playing the dark-skinned Simone. “Appearance-wise this is not the best choice,” the late singer’s daughter, Simone Kelly, told The New York Times. A tweet from Simone’s estate earlier this year demanded the actress “take Nina’s name out your mouth. For the rest of your life.”

The furor over “Nina,” which arrives in theaters April 22, is the latest in a series of Hollywood controversies over not just race but sexuality, gender and biological status. Hollywood has seen the pro-gay film “Stonewall” boycotted for marginalizing people of color, the transgender film “The Danish Girl” criticized for casting a non-transgender actor as its star, and the upcoming Marvel film “Doctor Strange” blasted for giving the role of an Asian male to Tilda Swinton.

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These vocal objections — along with the outcry over this year’s all-white Oscar acting nominees and complaints by actresses about lesser pay and opportunities — may seem like identity politics run rampant. But they clearly indicate a deep dissatisfaction with Hollywood’s approach to diversity. They also raise a question: Is the old Hollywood model of making crowd-pleasing movies with bankable stars — usually white ones — still working?

“Every year, people of color are increasing their population by half a percent,” says Darnell Hunt, a UCLA sociology professor who publishes a yearly report on diversity in the media. “Do the math, and within two decades the country will be more than half people who are minorities. The question we’re asking Hollywood is: ‘Whose stories are you really telling?’ ”

Problematic racial casting has a long history, from blackface (Laurence Olivier in “Othello”) to whitewashing (Kevin Spacey playing what was originally an African-American character in “Pay It Forward”). Mickey Rooney’s portrayal of I. Y. Yunioshi, a buffoonish Japanese man in “Breakfast at Tiffany’s,” raised few objections in 1961 but is now widely regarded as one of cinema’s most racist moments.

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The problems persist, says Guy Aoki, president of Media Action Network for Asian-Americans. He points to Emma Stone playing a Hawaiian in last year’s “Aloha,” the mostly European cast of this year’s “Gods of Egypt” and two characters in “The Martian” who were Asian in the novel but played by non-Asian actors (Mackenzie Davis and Chiwetel Ejiofor).

“I can see why it might seem a little nitpicky, but it’s important,” says Aoki. “You want to have Asian characters that people can relate to. If they can relate to an Asian person on television or film, then maybe they can relate to you in real life.”

Traditionally, Hollywood has countered that movies need established stars to turn a profit. Ridley Scott, criticized for using mostly white actors in another Egyptian fantasy film, “Exodus: Gods and Kings,” bluntly told Variety he could never get financing if he cast “Mohammad so-and-so from such-and-such.” Tom Hooper, director of “The Danish Girl,” said that Eddie Redmayne was always his first choice for the lead role of a person who undergoes one of the first sex-change operations.

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Nevertheless, the filmmaker Sean S. Baker found two transgender actresses, Kitana Kiki Rodriguez and Mya Taylor, to star in his acclaimed comedy-drama “Tangerine.” (It’s about two sex workers who track down a disloyal pimp.) Last year, “Tangerine” became the first film to launch an official Oscar campaign, backed by producers, for openly transgender actors.

“Trust me, I know the other side of the argument — I’m trying to make a film now where I can’t get money unless I have a star,” says Baker. “I’m not so unrealistic that I’m saying people should lose money just for the sake of integrity. But I am saying we could be smart enough as an industry to think around this stuff.”

LGBT filmmakers aren’t immune from criticism, either. The director Roland Emmerich is openly gay but outraged his community with “Stonewall” (2015), a drama based on the famous gay-rights riots in Greenwich Village in 1969. Although the riots were started by transgender blacks and Latinas, the film’s hero is a white Midwesterner (Jeremy Irvine). As a result, “Stonewall” was accused of whitewashing and became the target of an LGBT boycott.

The backlash against a gay director revealed racial biases and resentments that exist even within the close-knit gay community, says Faith Cheltenham, director of the wide-ranging bisexual advocacy group BiNet USA. “People ask me all the time: ‘You guys fight?’ I say, ‘Oh, yeah,’ ” says Cheltenham, who identifies as black and bisexual. “I see the gay community as a whole falling behind some of the expectations that mainstream society has about race.”

Overlooked in the debate is that films with diverse casts actually make money, according to Hunt, whose latest report for UCLA includes research on median global box-office receipts for 2014. That figure reached $122.2 million for the eight films with diverse casts (41 percent-50 percent minorities) but stalled at $52.5 million for the 55 films with non-diverse casts (less than 10 percent minorities).

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“People go to the movies to be entertained, but it’s also about politics. It’s about how people perceive you,” Hunt says. “That’s why people are so up in arms about every single movie in the industry.”