Since its founding in 1923, Disney has stood alone in Hollywood in one fundamental way: Its family-friendly movies, television shows and theme park rides, at least in theory, have always been aimed at , with potential political and cultural pitfalls zealously avoided.

The Disney brand is about wishing on stars and finding true love and living happily ever after. In case the fairy tale castles are too subtle, Disney theme parks outright promise an escape from reality with welcome signs that read, “Here you leave today and enter the world of yesterday, tomorrow and fantasy.”

Lately, however, real world ugliness has been creeping into the Magic Kingdom. In this hyperpartisan moment, both sides of the political divide have been pounding on Disney, endangering one of the world’s best-known brands — one that, for many, symbolizes America itself — as it tries to navigate a rapidly changing entertainment industry.

In some cases, Disney has willingly waded into cultural issues. Last summer, to applause from progressives and snarls from the far right, Disney decided to make loudspeaker announcements at its theme parks gender neutral, removing “ladies and gentlemen, boys and girls” in favor of “dreamers of all ages.” But the entertainment giant has also found itself dragged into the fray, as with the recent imbroglio over a new Florida law that among many things restricts classroom instruction through third grade on sexual orientation and gender identity and has been labeled by opponents as “Don’t Say Gay.”

At first, Disney tried not to take a side on the legislation, at least publicly, which prompted an employee revolt. Disney then aggressively denounced the bill — only to find itself in the cross hairs of Fox News hosts and Florida’s governor, Ron DeSantis, who sent a fund-raising email to supporters saying that “Woke Disney” had “lost any moral authority to tell you what to do.” Florida lawmakers began threatening to revoke a 55-year-old law that enables Walt Disney World to essentially function as its own municipal government. (Disney had already been at odds with the governor on pandemic issues like a vaccine mandate for employees.)

In trying to offend no one, Disney had seemingly lost everyone.

“The mission for the Disney brand has always been really clear: Do nothing that might upset or confuse the family audience,” said Martin Kaplan, the Norman Lear professor of entertainment, media and society at the University of Southern California and a former Walt Disney Studios executive. “Fun for all. Nothing objectionable. Let’s all be transformed by the magic wand. But we are so divided today, so revved up, that even Disney is having a hard time bringing us together.”

Avoiding socially divisive topics, of course, in itself reflects a certain worldview. The Walt Disney Company’s namesake founder, after all, was an anti-union conservative. Main Street U.S.A. patriotism is on prominent display at Disney’s theme parks. The traditional Christmas story is told each December at Disney World in Florida and Disneyland in California with Candlelight Processional events, Bible verses and all.

It took the company until 2009 to introduce a Black princess.

But in recent years, there has been a noticeable change. Robert A. Iger, who served as chief executive from 2005 to 2020, pushed the world’s largest entertainment company to emphasize diverse casting and storytelling. As he said at Disney’s 2017 shareholder meeting, referring to inclusion and equality: “We can take those values, which we deem important societally, and actually change people’s behavior — get people to be more accepting of the multiple differences and cultures and races and all other facets of our lives and our people.”

In essence, entertainment as advocacy.

Mr. Iger was the one who pushed forward the global blockbuster “Black Panther,” which had an almost entirely Black cast and a powerful Afrocentric story line. Under his tenure, Disney refocused the “Star Wars” franchise around female characters. A parade of animated movies (“Moana,” “Coco,” “Raya and the Last Dragon,” “Soul,” “Encanto”) showcased a wide variety of races, cultures and ethnicities.

The result, for the most part, has been one hit after another. But a swath of Disney’s audience has pushed back.

“Eternals,” a $200 million Disney-Marvel movie, was “review bombed” in the fall because it depicted a gay superhero kissing his husband, with online trolls flooding the Internet Movie Database with hundreds of homophobic one-star reviews. In January, Disney was accused by the actor Peter Dinklage and others of trafficking in stereotypes by moving forward with a live-action “Snow White” movie — until it was revealed that the company planned to replace the seven dwarfs with digitally created “magical creatures,” which, in turn, prompted complaints by others about the “erasure” of people with dwarfism.

Disney executives tend to dismiss such incidents as tempests in teapots: trending today, replaced by a new complaint tomorrow. But even moderate online storms can be a distraction inside the company. Meetings are held about how and whether to respond; fretful talent partners must be reassured.

As Disney prepared to introduce its streaming service in 2019, it began an extensive review of its film library. As part of the initiative, called Stories Matter, Disney added disclaimers to content that the company determined included “negative depictions or mistreatment of people or cultures.” Examples included episodes of “The Muppet Show” from the 1970s and the 1941 version of “Dumbo.”

“These stereotypes were wrong then and are wrong now,” the disclaimers read.

The Stories Matter team privately flagged other characters as potentially problematic, with the findings distributed to senior Disney leaders, according to two current Disney executives, who spoke on the condition of anonymity to discuss confidential information. Ursula, the villainous sea witch from “The Little Mermaid” (1989), was one. Her dark color palette (lavender skin, black legs) could be viewed through a racial lens, the Stories Matter team cautioned; she is also a “queer coded” character, with mannerisms inspired in part by those of a real-life drag queen.

Tinker Bell was marked for caution because she is “body conscious” and jealous of Peter Pan’s attention, according to the executives, while Captain Hook could expose Disney to accusations of discrimination or prejudice against individuals with disabilities because he is a villain.

At least some people inside Disney are concerned that such sensitivities go too far. One of the executives worried that looking at artistic creations through a “politically correct filter” could chill creativity.

Disney declined to comment for this article.

All of this comes at a perilous time for Disney, which is racing to remake itself as a streaming titan as technology giants like Amazon and Apple move deeper into the entertainment business and traditional cable networks like Disney-owned ESPN slowly wither. Disney is also coping with a disruptive changing of the guard, with Mr. Iger stepping down as executive chairman in December.

Mr. Iger occasionally spoke out on hot-button political issues during his time as chief executive. His successor, Bob Chapek, decided (with backing from the Disney board) to avoid weighing in on state political battles. Disney lobbyists would continue to work behind the scenes, however, as they did with the Florida legislation.

“Our diverse stories our corporate statements — and they are more powerful than any tweet or lobbying effort,” Mr. Chapek wrote in an email to Disney employees on March 7. “I firmly believe that our ability to tell such stories — and have them received with open eyes, ears and hearts — would be diminished if our company were to become a political football in any debate.”

In the case of Florida, the approach backfired, first with employee protests and a walkout and then with a right-wing backlash. The Fox News host Tucker Carlson said Disney had “a sexual agenda for 6-year-olds” and was “creepy as hell.” Tweets with the #boycottDisney hashtag accumulated millions of impressions between March 28 and April 3, according to ListenFirst, an analytics firm.

Disney executives have long held the position that boycotts have a minimal impact on the company’s business, if any. Disney is such a behemoth (it generates roughly $70 billion in annual revenue) that avoiding its products is almost impossible.

But the same vast reach that makes Disney hard to boycott also makes it an increasingly visible part of the country’s cultural debates. Hardly a month goes by without some kind of dust-up, usually with sexual identity and gender as the prompt.

Last summer, “Muppet Babies,” a Disney Junior series for children ages 3 to 8, gently explored gender identity. Gonzo donned a gown, defying a directive from Miss Piggy “that the girls come as princesses and the boys come as knights.” Out magazine wrote that the episode “just sent a powerful message of love and acceptance to gender-variant kids everywhere!” And a far-right pundit blasted Disney for “pushing the trans agenda” on children, starting an online brush fire.

Around the same time, some L.G.B.T.Q. advocates were criticizing Disney over “Loki,” a Disney+ superhero show. In the third episode of “Loki,” the title character briefly acknowledged for the first time onscreen what comic fans had long known: He is bisexual. But the blink-and-you-missed-it handling of the information angered some prominent members of the L.G.B.T.Q. community. “It’s, like, one word,” Russell T. Davies, a British screenwriter (“Queer as Folk”), said during a panel discussion at the time. “It’s a ridiculous, craven, feeble gesture.”

The fighting will undoubtedly continue: The Disney-Pixar film “Lightyear,” set for release in June, depicts a loving lesbian couple, while “Thor: Love and Thunder,” arriving in July, will showcase a major L.G.B.T.Q. character.

Last month, when Disney held its most-recent shareholder meeting, Mr. Chapek was put on the spot by shareholders from the political left and right.

One person called Disney to task for contributions to legislators who have championed bills that restrict voting and reproductive rights. Mr. Chapek said that Disney gave money to “both sides of the aisle” and that it was reassessing its donation policies. (He subsequently paused all contributions in Florida.) Another representative for a shareholder advocacy group then took the microphone and noted that “Disney from its very inception has always represented a safe haven for children,” before veering into homophobic and transphobic comments and asking Mr. Chapek to “ditch the politicization and gender ideology.”

In response, Mr. Chapek noted the contrasting shareholder concerns. “I think all the participants on today’s call can see how difficult it is to try to thread the needle between the extreme polarization of political viewpoints,” he said.

“What we want Disney to be is a place where people can come together,” he continued. “My opinion is that, when someone walks down Main Street and comes in the gates of our parks, they put their differences aside and look at what they have as a shared belief — a shared belief of Disney magic, hopes, dreams and imagination.”