They would not at first seem so different from you and me.

Teresa works in media and lives with an actress roommate. Kevin has a stultifying job but spends his off-hours watching “Portlandia” and devouring internet porn. Justin reads a lot of books and worries about the state of the country.

Yet unless you’re a hard-line Catholic conservative, you probably don’t have much in common with these people, who were undergrads together at Transfiguration College of Wyoming: an anti-abortion, anti-L.G.B.T. school where sex and cellphones (and federal funding) are forbidden .

And unless you live in an alternative theatrical universe programmed by David Mamet for The Heritage Foundation, you’ve probably never seen their like onstage.

That’s one of the things that makes Will Arbery ’s “Heroes of the Fourth Turning,” which opened on Monday at Playwrights Horizons, something of a red-state unicorn. The astonishing new play explores the lives and ideas of conservatives with affection, understanding and deep knowledge — if not, ultimately, approval.