“Soul Doctor,” the new Broadway musical about globe-trotting rabbi Shlomo Carlebach and his controversial friendship with jazz singer Nina Simone, opened Thursday night at Circle in the Square Theatre.

Reviewers largely hailed the lead performers, Eric Anderson and Amber Iman -- making her Broadway debut -- but had issues with the story, which several predictably joked could have used a “script doctor.”

Carlebach, a modern-day troubadour, escaped the Nazis as a child and came to America, where he embraced his heritage but found the traditions of modern Judaism too restrictive. He befriended Simone, “the High Priestess of Soul,” who introduced him to soul and gossip music, and went on to become a “Rock Star Rabbi,” who tended to his flock during the free-love era of the 1960s.

Anderson, who audience members will be surprised to learn isn’t Jewish, garnered a 2013 Drama Desk Award nomination for lead actor in a musical as the rabbi.

Here’s a look at what some of the top critics had to say:

Adam Feldman, Time Out New York: “The show’s opening number, in which a chorus of festively costumed ‘Holy Beggars’ streams down the aisles, promises a cross between ‘Fiddler on the Roof’ and ‘Hair.’ What follows, however, is mostly sentimental and familiar. The songs hold up well ... but the show digs shallowly into its central character and his beliefs, and often rings false.”

Charles Isherwood, The New York Times: “‘Soul Doctor’ is a bizarre and at times bewildering musical. Carlebach’s life certainly makes for a fascinating story, spanning as it does the divergent worlds of Nazi-occupied Austria and the free-loving Haight-Ashbury of the 1960s. But ‘Soul Doctor,’ which features Carlebach’s original music ... lays out Carlebach’s journey in mostly blunt, often hoary strokes ... As is often the case with bio-musicals, we learn the notable turns of the man’s life ... without really exploring his depths.”

Elysa Gardner, USA Today: “The musical’s mix of hokey humor and preachy sentimentality is bound to test the most altruistic spirit ... It opens in 1972, at a concert in Vienna, where Simone introduces our hero as ‘my soul brother-from-another-mother.’ We then flash back to Vienna in 1938, where (Reb) Pinchas is leading young Shlomo and his brother in Torah study. ‘Being a Jew is about pain and suffering!’ he barks at them. ‘Joy is for Gentiles.’ The cliches pile on ...”

Elisabeth Vincentelli, New York Post: “Carlebach is presented as a kind of holy fool, at once persistent and naive. Asked by his music producer, Milt, if he’s heard of Peter, Paul and Mary, Carlebach replies, ‘I don’t know so much the New Testament.’ ... You often wish ‘Soul Doctor’ had called a script doctor -- especially when Shlomo’s warned that he’s ‘gonna do the horah/In Sodom and Gomorrah.’ To which even a gentile might sigh, ‘Oy vey.’”

See TheaterMania’s video from the press meet-and-greet, below.

“Soul Doctor,” at Circle in the Square Theatre, 1600 Broadway, for an open-ended run. Rickeys: $135. Call 212-239-6200.

Follow Robert Kahn on Twitter@RobertKahn