Rachel Dratch and Daniel Radcliffe in “Privacy,” a play where audience members are asked to turn on their cell phones. PHOTOGRAPH BY JOAN MARCUS / THE PUBLIC THEATRE

Most theatregoers I know have an almost physical aversion to audience participation. That’s probably because audience members are often cast in the role of patsy—set up to look awkward, outsmarted, or nervous, whether they’re being dragged onstage by a tuxedoed magician or simply asked to give a “show of hands.” Or maybe we just like to let our imaginations take over in the dark, free of self-consciousness. If you are one of those people, “Privacy,” which just opened at the Public Theatre, will make you squirm. But that’s the point. Its subject is the vast amounts of data we unthinkingly put online, something we tend to be vaguely concerned about, in the abstract, but complacent about in our everyday lives. Once we’re assembled in a theatre, with the house lights on, the risks of self-exposure are harder to shrug off.

The show, which originated at London’s Donmar Warehouse and was conceived by James Graham and Josie Rourke, begins with an announcement by Oskar Eustis, the Public’s artistic director: “In order that people around you can enjoy the performance, we ask that you turn your phone . . . on.” Actually, leaving your phone on is the least of it. At various points, audience members are asked to take selfies, share their Uber ratings, and Google “pizza.” Easy enough. But these audience-hacking moments escalate in ways that are meant to creep us out and wake us up. We’re told—rather, shown—how intrusively specific our “metadata” is, from targeted advertising to an iPhone feature called “Frequent Locations.” (Settings -> Privacy -> Location Services -> System Services -> Frequent Locations. Whoa, right?) Upstage left, a concierge-looking fellow sits behind a laptop, manipulating what information he can gather about specific audience members, who are asked for consent when they order their tickets. The implicit question: If you’re embarrassed watching your online footprint splashed across an LED screen in front of three hundred strangers, do you really want it out there for the whole world to see?

Now would be a good time to mention that “Privacy” has a plot, and that it stars Daniel Radcliffe, who is cutely fretful in the role of the Writer, a depressed bisexual playwright smarting from a breakup. In the first scene, he complains to his therapist (Reg Rogers) that he’s “hyperlinking through life,” after his ex told him that he was “too closed.” This leads him on a journey to New York to “open up” via his smartphone, though it’s a little hazy how that’s supposed to work. He has only one Twitter follower—is this the key to his loneliness? During his quest, various experts appear as spirit guides, from the tech-wary M.I.T. professor Sherry Turkle to the OkCupid co-founder Christian Rudder. Their words are culled from published materials and original interviews, and they’re played by a shape-shifting cast, including De’Adre Aziza and Rachel Dratch. There’s an easygoing absurdism to these encounters, reminiscent of Woody Allen’s one-act play “God.” Ujala Sehgal, of the New York Civil Liberties Union, shows up in the Writer’s living room to talk about police vans outfitted with warrantless X-ray vision. Randi Zuckerberg (sister of Mark and author of “Dot Complicated”) materializes on a barstool to talk netiquette. Others drop in with paranoia-inducing disclosures: Did you know that Burberry can track the clothes on your back? Could your Xbox be spying on you?

Reported on the evening news, these concerns might seem overblown, but, deployed like high-tech magic tricks, they have a tada! effect. (Some old-school theatrical trickery is employed as well, but I won’t say more.) In the second act—after a detour through the online-dating world—we get into N.S.A. territory, with cameos by the likes of Edward Snowden and James Comey. The tone gets ominous, the revelations darker. But “Privacy” never goes in for the kill. Just when we reach the highest halls of government, the play reverts to the contrived tale of the Writer’s romantic travails, which, despite Radcliffe’s movie-star charm, never come off as real or psychologically coherent. The Writer is less a character than a device, in a show that is ultimately nothing but devices, whether handheld and theatrical. The production has the smoothness of a TED talk and the gentle humor of a romantic comedy, but there’s no pull-back-the-curtain moment to truly freak us out, or stage poetry to lift the piece beyond mild provocation. It’s lightweight agitprop: unsure, like the rest of us, just how seriously it should take its subject.

Something ontological has changed with our surrender of privacy—The New Yorker’s Jill Lepore, also a character in the play, dives into it here—and perhaps that’s more unsettling than any nefarious government data-suck. But perhaps not. All it takes is a change in the political winds for the queasy-making to become the truly terrifying. “Privacy” doesn’t give us a dystopian future, just a funhouse tour through the present. (And a timely one, during a month when more than fifteen million users handed over suspiciously broad access to the makers of Pokémon Go.) I will credit it with this much, though: as soon as I left the theatre, I disabled “Frequent Locations” on my iPhone.