ALEXANDRA PELOSI’S latest HBO documentary, “Friends of God,” will doubtless garner some attention for her fortuitously timed interview with Pastor Ted Haggard, the disgraced head of the National Assn. of Evangelicals. Interviewed prior to allegations that he purchased illicit drugs and had sex with a male prostitute, Haggard boasts about evangelicals’ rollicking sex lives and ironically contemplates the harm done when their leaders experience moral lapses.

Yet another theme threaded throughout this hourlong production, which premieres Jan. 25, is of greater import to the entertainment industry — namely, whether Hollywood can befriend the sprawling evangelical movement or must accept it as a lost cause.

For a group that professes to know with irritating certainty what happens after death, evangelicals clearly feel shortchanged by the media here on Earth, which they approach with a sizable chip on their shoulders. In “Friends of God,” Pelosi — the daughter of House Speaker Nancy Pelosi — hits the road to provide an up-close glimpse of evangelism, catching Haggard drawing knowing chuckles during a sermon by saying, “We still have a problem with Hollywood.” Self-described Christian comic Brad Stine also fumes over how most entertainment overlooks evangelicals — partially demonstrated, in his view, by the fact nobody has offered him a primetime sitcom.

ON ITS FACE, bypassing evangelicals is a sane-enough response to a group whose most vocal spokespeople deal in the kind of absolutes that make any deviation an affront to their values. Given the likelihood dramatic interpretations of religion will unleash their wrath, it’s easy to conclude life’s too short to bother. Moreover, Pelosi’s footage of schoolchildren being indoctrinated to believe in creationism and that evolutionary theory is a crock stirs doubts regarding whether it’s possible to rationally engage those who want to dial back scientific knowledge to the 19th century.

Nevertheless, there are tens of millions of evangelicals out there (Pelosi’s film estimates their numbers at 50 million to 80 million in the U.S.), possessing purchasing power stunningly demonstrated by “The Passion of the Christ.” From a practical standpoint, the Christian market thus appears too bountiful to ignore, which explains the furtive attempts to establish film labels catering to this niche.

Bridging the gap, however, will require a serious dialogue — one that hinges on separating those who specialize in the business of outrage from evangelicals who, despite misgivings, genuinely want to be part of the larger media culture.

From that perspective, there has been something particularly noteworthy about NBC’s “Studio 60 on the Sunset Strip,” as series creator Aaron Sorkin persists in bluntly tackling this schism head-on — using his bully pulpit to poke his thumb in the eye of “media watchdogs” poised to protest any perceived slight, while simultaneously putting a sympathetic face on Christians in the character of Harriet Hayes (Sarah Paulson).

Not all evangelicals view Hollywood as the enemy. Take Mastermedia Intl., which consults on media issues pertaining to Christianity and even prays for key executives and stars. (Assembled alphabetically, the 2007 daily “prayer calendar” kicks off with producer J.J. Abrams and Fox News Channel CEO Roger Ailes.)

THE MEDIA does itself no favors, then, by painting all evangelicals with the same broad brush. Nor does the big-city elite’s thinly veiled condescension help, as is evident within the Pelosi documentary, in which she pursues the whole exercise with a slightly bemused demeanor, as if she has just parachuted onto the dark side of the moon.

“There’s something very strange about these people — they’re all very happy!” she gushes at one point.

No amount of wooing will fully assuage the lack of trust between Hollywood and evangelicals, and as the documentary makes clear, the deeply religious have gone about creating their own leisure alternatives — with everything from theme parks and miniature golf courses to wrestling and standup comics.

Reading between the lines, though, there ought to be room for middle ground: For while many evangelicals clearly derive comfort from having an earthbound foe to demonize, not all of them want to be ridiculed, dismissed and cut off from pop culture. Studios, meanwhile, covet their business, and if there’s one enduring truth about Hollywood, it’s that you don’t need to see eye to eye on everything to take somebody’s money.