Hedwig (Euan Morton) in “Hedwig and the Angry Inch,” which is about a rocker in drag who was born a boy but, because of a botched operation, has been cast into gender limbo. (Joan Marcus)

John Cameron Mitchell and Stephen Trask were just starting to figure out who Hedwig Schmidt was back in 1997, when, in a clubby little space in the West Village, I had the first of many encounters with “Hedwig and the Angry Inch.” Twenty years on, I’m amazed at how audiences are still discovering her, still seeing the boldness and freshness in one of the most outrageous characters ever to headline in musical theater.

 It’s a longevity no one could have predicted, certainly not Mitchell and Trask, the book writer/original star and the composer of the intellectually ambitious punk-rock musical that introduced the world to a brooding, “internationally ignored” song stylist doomed to fame and fortune’s “discard” folder. “Hedwig,” now ensconced at the Kennedy Center, featuring Euan Morton in the title role, tells the story of an émigré glam rocker in drag, born a boy in then-East Berlin but by virtue of a botched sex-change operation has been cast into a kind of gender limbo (giving special meaning to the title of the band that backs her up, the Angry Inch).

Since its off-Broadway debut in 1998, the irreverent concert-style show has been produced countless times around the world: In Seoul, a production has been running for 12 years. But not until it finally reached Broadway in 2014, in a version that won four Tony awards, including one for its star, Neil Patrick Harris, did “Hedwig” provide any serious financial return to its creators — a sign of how precarious and marginally profitable sitting out on the cutting edge can be.

“There was never any real money in it until Broadway,” Mitchell says by phone from Los Angeles, where he’s in the midst of meetings, pitching a musical-themed project for television.

“Stephen and I were never fully accepted when it first came out. There was a kind of uptown disdain for it. Even the film [released in 2001, with Mitchell as Hedwig, and Miriam Shor, reprising her role as sidekick Yitzhak] was a flop at first. Like the character, we had to claw our way to respectability.”

The long road to “respectability” could actually be considered a badge of integrity for this funny, salacious, shabby-chic 90-minute show, embroidered by Trask’s heart-melting Top-40 pop ballads (“Wig in a Box,” “Wicked Little Town,” “Midnight Radio”) and acid-rock numbers (“Angry Inch”). That awkward climb is an indication, too, of just how ahead of its time “Hedwig” was. 

Before some of the complexities of gender identity became a fascination for the media, or the fight for the rights of transgender people and others on the fringe began to be taken seriously by the political mainstream, there was “Hedwig.” The show came into being as a satire of popular culture and a poignant contemplation of the human need to define one’s place in the world. Riffing on a Platonic notion of self, the musical revealed how anguishing the quest for self could be, exposing us through song and metaphor to all the contradictions in Hedwig’s tormented psyche. 

A connection is drawn, for example, between the ambiguities in Hedwig’s sexual identity and the partition of the country of his/her birth. The musical suggests that the coexistence of communist East Germany, where Hedwig was born to a German woman and an American G.I., and democratic West Germany, is a link to unraveling another mystery: the metaphysical tie between Hedwig and a young rocker she’s mentored, Tommy Gnosis, who’s unseen in the stage version and who has found the fame and acclaim that embittered Hedwig never does.

“I was learning from the ­gender-bending queens of the club [scene], just watching in awe and wondering why they weren’t stars,” Mitchell says, describing the inspiration for the character he wrote for himself. It intrigued him, how drag performers remained so marginalized in New York when in other countries — Britain, Australia, Japan — “cross-gender performance is an ancient tradition.” Here, he adds, “they were sort of third-class citizens. Their lives were already punk rock.”

Trask, who’s now based in Lexington, Ky., and regularly composes movie scores (“The Savages,” “Little Fockers,”), says the re-injection of “Hedwig” into the culture, first via Broadway and then the national tour that ends at the Kennedy Center, occurred after he and Mitchell performed together in 2007 in Seoul, for a concert that reunited 10 actors who played Hedwig there. “We had such a good time, we felt reconnected,” Trask says, in an interview in a studio in Manhattan he’s using to work on his latest project, a musical about the Studio 54 nightlife culture of the late 1970s and early ’80s called “This Ain’t No Disco,” that is to be produced by New York’s Atlantic Theater Company.

The composer had the idea of recruiting Harris for a revival of “Hedwig.” “My first harassing email was in 2008 or ’09,” he says, adding that he later told the actor, known mostly for his television work, “If this role was written for anyone but John, it was written for you.” Although it would take half a decade for the Broadway incarnation to come into being, under the direction of Michael Mayer, the material held up and still felt a little dangerous.

“It was Neil bringing his star power and ambassadorship, telling people it wasn’t going to scare them,” Mitchell says.

You get the firm feeling, recalling the electric impression Mitchell himself made in the role, how influential “Hedwig” truly has been. The show helped give license to composers and librettists to bring to center stage all manner of rebels and iconoclasts and oddballs and damaged types, from the sexually repressed teenagers of Steven Sater and Duncan Sheik’s “Spring Awakening” (2006) to the mentally ill mom of Tom Kitt and Brian Yorkey’s “Next to Normal” (2008) to the anxiety-ridden ­antihero of “Dear Evan Hansen” (2016).

“Everyone I care about, I met because of it,” Mitchell says. “It even allowed me to pay for my mom’s Alzheimer’s care.” All triggered by a desire he and Trask had, to take a flamboyant character wherever she needed to go.

“I just thought,” Mitchell recalls, “‘Damn, a musical can be anything.’ ”

If You Go
Hedwig and the Angry Inch

Kennedy Center, 2700 F St. NW. 202-467-4600. kennedy-center.org.

Dates: Through July 2.

Tickets: $59-$159.