In late February, actor Dennis Quaid joined religious rock group MercyMe at a Dallas concert to sing — and promote his new movie. The band has toured for much of the last year in support of the new film “I Can Only Imagine,” which tells the story of how lead singer Bart Millard wrote the bestselling Christian single ever after the death of his father. For a biblically minded movie to succeed in theaters, it used to be enough to screen the film for pastors months ahead of time and create study guides for campus youth groups. Studios now have to go to greater lengths to attract devout audiences in an increasingly challenged faith-based film business, as the market for Christian movies becomes more crowded. “Because there have been so many movies made for this audience, they have become much more discerning,” said Howard Cohen, co-founder of Roadside Attractions, the distributor of “I Can Only Imagine.” “And they will choose the ones that not only have a strong, Christian message but are bigger-feeling, more studio-type films.” Just a few years ago, the faith-based genre produced multiple surprise hits as studios ramped up investment in religious-themed movies, resulting in successes such as “Heaven Is for Real” and “God’s Not Dead.” The rate of faith-based films released in theaters annually has doubled since 2012 to about 12 a year. But the genre is now in a surprising slump.