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.”