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The subject in this case is heartland homophobia. A quick Twitter search leads Dee Dee and Barry to the perfect object for their insincere concern: a 17-year-old lesbian whose high school won’t let her bring a girl to the prom. (The theater executive Jack Viertel came up with the idea after reading about several similar cases, including one in Mississippi in 2010.) Dragging along their exasperated press agent, the four vain actors hitch a ride to Indiana with a bus-and-truck tour of “Godspell,” hoping to rekindle their careers by wowing the “Jesus jumping losers and their inbred wives” into submission.

“We’re gonna help that little lesbian,” Barry sings, “whether she likes it or not.”

Like segregation in “Hairspray” — or, for that matter, racism in “South Pacific” — anti-gay intolerance offers a comfortable target and a teachable moment. Sincerity can be dangerous for comedies, though, burning away laughs and landing everyone in a lake of treacle.

If that problem is mostly avoided here, it is at a slight cost to depth and texture. Emma, the girl at the center of the storm, turns out to be a perfectly adjusted young woman with no satirical qualities except in her wardrobe. (The hilarious costumes are by Ann Roth and Matthew Pachtman.) Though smartly played by Caitlin Kinnunen, and provided with intolerant parents we never meet, the character as written is something of a blank.

That seems strategic to me. The lovely romantic ballads Emma is given to sing, with titles like “Dance With You” and “Unruly Heart,” are completely anodyne — or would be if it weren’t for the context, which turns them into breakthroughs.

But the other Indianans are blurrier, as if the authors couldn’t quite decide how much ribbing they could take. The local teenagers might as well be from “Bye Bye Birdie” — and they evolve from antagonists to allies with the scantest provocation. Even the school principal (Michael Potts) turns out to be unflappably noble; more surprising, as Dee Dee discovers, he’s a fan of hers and yet straight.