Mr. Bock, who is Presbyterian, is credited with being the first Hollywood marketer to realize that churches had started to install enormous screens to use during their services, sometimes just to display hymn lyrics. More recently, $35,000 video walls have become more common in sanctuaries. “It makes church feel more contemporary,” Mr. Bock said, adding that ministers are becoming adept at “building vibrant social media communities that expand their reach far beyond Sunday morning.”

The Rev. Roderick Dwayne Belin, a senior A.M.E. Church leader, stood before a gathering of more than 1,000 pastors in a drafty Marriott ballroom in Naperville, Ill., this month and extolled the virtues of a Hollywood movie.

“Imagine this clip playing to your congregation, perhaps tied to a theological discussion about our sacred lives and our secular lives and how there is really no division,” he said, before showing the trailer for “Hidden Figures,” which 20th Century Fox will release in theaters nationwide on Jan. 6.

The film has no obvious religious message. Rather, it is a feel-good drama about unsung black heroines in the NASA space race of the 1960s. But Fox — working with a little-known firm called Wit PR, which pitches movies to churches — sought out Mr. Belin to help sell “Hidden Figures” as an aspirational story about women who have faith in themselves. He became a proponent after a visit to the movie’s set in Atlanta, where Wit PR invited seven influential pastors to watch filming and hang out with stars like Kevin Costner and Taraji P. Henson, who spoke of her own struggles to succeed in Hollywood.

“I came away really interested in using film to explore faith,” Mr. Belin said.

On the surface, Hollywood is a land of loose morals, where materialism rules, sex and drugs are celebrated on screen (and off), and power players can have a distant relationship with the truth. But movie studios and their partners have quietly — very quietly, sometimes to the degree of a black ops endeavor — been building deep connections to Christian filmgoers who dwell elsewhere on the spectrum of politics and social values. In doing so, they have tapped churches, military groups, right-leaning bloggers and, particularly, a fraternity of marketing specialists who cut their teeth on overtly religious movies but now put their influence behind mainstream works like “Frozen,” “The Conjuring,” “Sully” and “Hidden Figures.”

The marketers are writing bullet points for sermons, providing footage for television screens mounted in sanctuaries and proposing Sunday school lesson plans. In some cases, studios are even flying actors, costume designers and producers to megachurch discussion groups.

Hollywood’s awareness of its need to pay better attention to flyover-state audiences has grown even more urgent of late, as ultraliberal movie executives, shocked to see a celebrity-encircled Hillary Clinton lose the presidential election to Donald J. Trump, have realized the degree to which they are out of touch with a vast pool of Americans. Tens of millions of voters did not care what stars had to say in support of Mrs. Clinton.

Are those voters also ignoring the likes of Leonardo DiCaprio and Meryl Streep when they promote movies? Would they listen if it were a church leader telling them to buy a ticket instead?

Film companies can no longer afford to take any audience for granted. Despite a growing population, North America’s movie going has been more or less flat — not exactly what investors want to hear. Last year, 1.32 billion tickets were sold, up from the year before but down from the 10-year high of 1.42 billion in 2009, according to the Motion Picture Association of America. More troubling, cheaper and more convenient in-home entertainment options are threatening the grip that multiplexes have long had on young adults; the number of frequent moviegoers ages 12 to 24 has fallen for three consecutive years.

Hollywood is under pressure to reverse that trend. Churches may seem like an unusual path toward young people, but 41 percent of millennials engage in some form of daily prayer, according to a 2010 Pew Research paper. To reach them, many ministers have built vast social media networks. The Rev. Jamal H. Bryant, a megachurch pastor in Baltimore, has 250,000 followers on Twitter. (His church also has a smartphone app.)

Studios used to sell movies by bombarding television networks with advertising on the eve of release. That tactic is still used for summer blockbusters, but it is expensive and increasingly ineffective in the DVR age. As a result, studios are aggressively trying to plumb niche markets that can be reached through word of mouth.

Francis Parq of Los Angeles during a screening of the documentary “Hillsong: Let Hope Rise” at ArcLight Hollywood theater in Los Angeles. Credit Jenna Schoenefeld for The New York Times

In the coming weeks, Mr. Bryant plans to bring up to 300 parishioners to a Wit PR-organized screening of “Hidden Figures” in Northwest Baltimore. Afterward, Mr. Bryant intends to lead a discussion connecting the plot to a theological message.

“Most studios, to be honest, have no idea how to market to us,” Mr. Bryant said. “They’re still doing the Sammy Davis Jr. tap dance: ‘Look at me! Aren’t you impressed?’ Well, no, not really. But if you bring us into the tent, we are often excited to spread the word.”

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