Sholem Asch is having a year.

The controversial Yiddish writer’s early 20th-century play, “God of Vengeance,” landed its cast in court on charges of obscenity when it opened at the 42nd Street Apollo Theater in 1923, but the zeitgeist has caught up with it. Now, when same-sex relationships generally are accepted, the love between two young women shown in the play is at the heart of Paula Vogel’s charming and touching musical production about Asch’s scandalous work.

In “Indecent,” now at the Cort Theatre, the Pulitzer-Prize winning Vogel (“How I Learned to Drive”) and her co-creator and director, Rebecca Taichman, bring to the stage the story of how Asch’s play, which he wrote in Warsaw in 1906, when he was just 26 years old, became a hit all over Europe, attracting the leading stars of Yiddish theater, but ran into censorship problems when it opened “uptown” in Manhattan in an English translation. The play marks the Broadway debut of both Vogel and Taichman, although the two women have long and lauded theater resumes. Both first came across “God of Vengeance” when they were students, and Taichman used the play as a basis for her senior thesis at Yale School of Drama.

Brilliantly staged by Taichman, “Indecent” intersperses scenes from Asch’s life and career with musical numbers set in European capitals and some short scenes from the original play itself. It makes ingenious use of projections to indicate the language spoken and occasional chronological time shifts. Vogel’s focus is on the primacy of the love between Rifkele and Manke, characters in Asch’s play, but also on the power and potency of art, on its ability to entertain and ennoble. That comes through most clearly in the character of the stage manager Lemml, radiantly performed by Richard Topol, who gives up a predictable life as a tailor to devote himself to the theater and to Asch’s great work, an experience that gives his life dignity and meaning.

In “God of Vengeance,” which received an excellent revival recently from the New Yiddish Rep at La MaMa, a brothel owner seeks to gain respectability in the community by commissioning the writing of a sefer Torah and making a good match for his teenage daughter, Rifkele. The truly daring aspects of Asch’s play are its searing indictment of communal and religious hypocrisy, phenomena that are just as common today as they ever were, and in all faith communities. (Think Ivan Boesky and Bernie Madoff, Ted Haggard and Jimmy Swaggart.) The rain scene in the play, where Rifkele and Manke share a kiss, must have been a shocker, but their relationship remains a subplot in the play as a whole.

Vogel and Taichman put that relationship front and center; they imbue it with the sweetness of the girls’ love and also with the symbolic weight of the prejudice and small-mindedness they encounter. The two women take on the mantle of European Jewry, also despised and threatened by a hate-filled enemy. In “Indecent,” Asch is psychologically and artistically crippled by his visits to Poland and the rising anti-Semitism he sees happening there. When he does not participate as vigorously in the defense of his play as Lemml believes he should, the stage manager quits in disgust. That sounds a warning to the theater troupe on stage, as well as to the audience. The forces of repression are abroad in the land, and they must be confronted.

The Broadway cast of “Indecent” has been together since the play’s successful run off-Broadway at the Vineyard Theatre, and they perform as smoothly as you’d expect from such a long-term ensemble. The play’s composers, Lisa Gutkin and Aaron Halva, play instruments onstage with some of the actors, and sometimes dance with the cast. Music and movement, choreographed by David Dorfman, are used so effectively in the production that they serve to deepen the joy and pathos rather than trivialize it.

It is a stunning achievement and a reminder of the full-on theater experience Jewish immigrants enjoyed in the Yiddish theater. Asch must be smiling somewhere.