In the first scene of “Caroline,” a thoroughly lovely new play by Preston Max Allen, a woman and her young daughter sit in a diner. The child, who is just shy of 10, apparently has a broken arm, and their conversation suggests they are running from something, or someone. At one point, the mother, Maddie, asks, “Do you have any thoughts on what you want your name to be?”

Your first guess might be that these two have entered some kind of witness protection program. But after we follow Maddie and Caroline, as the daughter opts to call herself, to a hotel room, it becomes clear — spoiler alert, for those who wish to go in totally cold — that this is not the case. Caroline is a transgender girl, and while Maddie has a complicated history, involving a lot of bad choices, it was her child’s decision to no longer identify as a boy that has led to their current predicament.

“Caroline” follows its title character — played by River Lipe-Smith, an extraordinary young actor who identifies as non-binary — and Maddie, portrayed by Chloë Grace Moretz, a former teen star who began acting as a child and is just as compelling here, as they seek refuge with Maddie’s mom, Rhea. Grandma is described in the stage directions thusly: “Comes from wealth. Warmth is not intuitive for her, but it’s not entirely out of reach.” 

What’s most beautiful about Mr. Allen’s one-act piece, in fact, is how it takes subject matter that another playwright might have used to preach (to the converted) or demonize a subset of people and creates a complicated, surprising story in which all of the characters approach a difficult situation with basically good intentions. 

The cherry on top is the director of this production: David Cromer, a prolific and versatile artist (also a fine actor) who has shown a particular affinity for guiding ensemble pieces in intimate settings. His company here is completed by Amy Landecker, who like Ms. Moretz is best known for her screen work; the older actress’s chiseled, well-preserved beauty helps reinforce our first impression of Rhea as chilly and elusive. 

Mind you, Maddie has put her mother through an awful lot, and Rhea’s reactions to the twists that have brought her daughter and grandchild to her house, and the solutions she proposes, aren’t what you’d necessarily expect them to be. When Rhea assures Maddie at one point, referring to herself and Maddie’s father, “We’re not Republicans,” it’s both an ironic explanation and a very timely reminder that people should not be judged by their political affiliations.

The most radical element of “Caroline,” and the greatest source of conflict in the play, is not the title character’s gender transition, but Maddie’s insistence on finding purpose through motherhood. Mr. Allen doesn’t gloss over the factors that make Rhea worried about the challenges her daughter faces, but the connection between Maddie and Caroline is so ripe with love, expressed in ways both goofy and profound, that we not only root for them but feel increasing optimism, despite the considerable odds they face.  

The actors make this relationship so accessible that it alternately soothes and stings. River Lipe-Smith, who is only 11, is especially remarkable in capturing the curiosity and pure candor exclusive to the very young, however precocious. When Caroline earnestly admits her mother’s youthful transgressions were “pretty bad,” or later, when she tells Maddie, “You don’t need to be better. I like how you are,” you may find yourself caught between laughter and tears.

And when Maddie describes Caroline, in an angrier exchange with Rhea, as “my foundation,” you may feel like cheering — whether you’re a stay-at-home mom or, like Maddie, a single working mom, or you don’t have kids at all. The humanism that defines “Caroline” is that inclusive, and it will do no less than lift your heart.