NEW YORK — When Janeane Garofalo asked Brad Bird, the director of “Mission: Impossible — Ghost Protocol,” about Tom Cruise at a recent Tribeca Film Festival event, she peppered Bird with allusions to the Scientology documentary “Going Clear.” Bird called it “a very inside reference,” but Garofalo quickly disagreed.

“Not anymore,” she said. “That documentary … wooo! ‘Going Clear,’ we could talk about that all day!”

That’s probably not what Tom Cruise or the makers of the next “Mission: Impossible” film, “Rogue Nation,” want to hear. “Going Clear: Scientology and the Prison of Belief,” Alex Gibney’s documentary based on the book by the Pulitzer Prize-winning journalist Lawrence Wright, was a revelation to many and a certain challenge to Cruise, who in recent years has quieted his public advocacy for Scientology.

The film and book did more than anything before to expose the secretive organization and detail some troubling claims involving Cruise, Scientology’s most famous face. Cruise has yet to say anything publicly about “Going Clear,” a silence that may be difficult to maintain, given the high-profile demands of promoting a summer blockbuster hoping to make some $700 million worldwide.

Cruise’s stardom has long had a Teflon indestructability, having survived one of the most notorious of public-relations disasters in 2005 when he ditched his longtime publicist for his sister, Lee Anne DeVette, a Scientologist; dramatically wooed his eventual third wife, Katie Holmes; and jumped on Oprah Winfrey’s couch.

Ten years later, a documentary may be a seemingly small threat to a global star who has already weathered media storms over his Scientology beliefs. Or “Going Clear” could persist as an acute challenge to Cruise at a time when his box-office clout may be waning and in a media age where privacy seldom lasts.

The impact of “Going Clear” has also been unusually large. When it aired on HBO on March 29, shortly after premiering in theaters, it became a trending topic on Twitter. Critics called it a “powder-keg” and a “scorching takedown of Scientology.”

Wright and Gibney insist Scientologists are free to believe what they want, but maintain the church should be held accountable for what they claim is frequently abusive treatment. The filmmakers have pressed for change in either Scientology’s tax-exempt status or through its influential celebrity figureheads: Cruise and John Travolta.

“There aren’t very many alternatives and law enforcement agencies are stymied,” says Wright. “What’s left is for journalists to call attention to what’s going on and at least inform people. We certainly are singling out some celebrities because they bear a moral responsibility and we’re making certain that they have to recognize that.”

Travolta reacted in an April interview while promoting his latest film, “The Forger.” He told The Tampa Bay Times that he wouldn’t watch a documentary “so decidedly negative” when his decades as a Scientologist have been “nothing but brilliant for me.”

“I haven’t experienced anything that the hearsay has (claimed), so why would I communicate something that wasn’t true for me?” Travolta told the paper. “It wouldn’t make sense, nor would it for Tom, I imagine.”

Cruise’s representative did not respond to requests for comment for this article. The Church of Scientology has called the documentary “a one-sided false diatribe” reliant on the testimony of “bitter, vengeful apostates.”

When the trailer for “Rogue Nation” debuted in late March, concerns about Scientology took a back seat to Cruise’s movie stunt prowess. The clip, which has already been watched by more than 7 million on YouTube, featured the remarkable sight of Cruise hanging off the side of an airplane at liftoff — a stunt Cruise performed himself.

Few theater owners at their annual CinemaCon convention in Las Vegas, where Cruise previewed the film, appeared concerned about his drawing power.

“As long as he makes a good film, people are going to come watch it,” said Morris Schulman, president of Texas’ Schulman Theaters Inc. “‘Mission: Impossible’ is a great franchise and we’re excited to have it this summer. Hanging on that plane? That’s pretty spectacular. That’s cool.”

But some believe Cruise is facing a crossroads. Jeetendr Sehdev, a marketing professor at the University of Southern California and a celebrity branding expert, says people feel increasingly uneasy about Cruise and that his kind of “contrived celebrity” is outdated.

“The documentary is going to have an impact on ‘Mission: Impossible’ when it comes out,” says Sehdev. “Secrets in Hollywood are really no longer sexy. Audiences are looking for transparency and authenticity in their celebrities more than ever before.”

“Mission: Impossible — Ghost Protocol,” which is scheduled for release on July 31, reunites Cruise with Christopher McQuarrie (director of “Jack Reacher” and screenwriter of “Valkerie” and “Edge of Tomorrow”), and comes on the heels of several underperforming releases from the 52-year-old actor. His last three films — “Jack Reacher, “Oblivion” and “Edge of Tomorrow” — have failed to crack $100 million at the North American box office.

While Sehdev believes it’s imperative for Cruise to address “Going Clear” and to refashion his image for media-savvy millennials, Amy Nicholson, film critic for LA Weekly and author of “Tom Cruise: Anatomy of an Actor,” thinks “it’s unfair that we obsess over this religion and this church when he obviously believes it very much.”

Instead, Nicholson says Cruise needs a makeover not in public relations, but movies.

“I get frustrated with the last decade of his career,” she says. “He’s not doing ‘The Color of Money’ anymore; he’s doing the ‘Mission: Impossibles.’ I think he feels sort of cornered. He needs to prove that he’s the biggest box-office star in the world again before he goes back to acting.”