The answer below is taken from a previous answer of mine from a few years back, answering a question asking if it was controversial, rather than asking why it was so successful. This is a slightly different question, but they're reasonably similar answers in some ways, because of course, the principle of 'all publicity is good publicity' applies to some extent. However, to some extent the question is unanswerable; if record company executives knew why some things sold like hotcakes and other things sold poorly, they'd ....have hits more reliably, I suppose. Anyway, the answer (originally from here) is here:

For context of the readers here, Jesus Christ Superstar - usually experienced as a musical these days, or perhaps the film - was released first as an album in the 'rock opera' tradition of Tommy or Quadrophenia by The Who - the backing band on the 1970 album was basically Joe Cocker's backing band, and Ian Gillan of Deep Purple played Jesus, while the former lead singer of Manfred Mann played Herod. Though it clearly had much more of a musical theatre bent than anything The Who wrote; Murray Head who played Judas came to do Superstar straight from a run of the rock musical Hair.

The original album was tremendously successful in the US, where it hit #1 in February 1971. It opened as a Broadway musical in October 1971 which had very healthy presales given its success as an album; oddly in Webber and Rice's native Britain, the album seemed much less successful initially, and it was only after it opened in the West End in 1972 that it got into the British charts.

Is Superstar a cynical attempt to cash in on the current “counterculture” trend toward religiosity? Is it a gigantic put-on, and will the authors come forward and confess after salting away their fust five million? Is it a naive but honest work inspired by true religious feeling but hamstrung by lack of talent, taste and comprehension? Or is it merely a fluke-a shoddy piece of hackwork brought to prominence by a combination of timeless and clever, massive merchandizing?

So asked Dan Morgenstern in an issue of the jazz-focused music magazine Down Beat, in 1971 (i.e., he was talking about the album/play, rather than the film).

The reason Superstar was being discussed in Down Beat was because, as James R. Huffman pointed out in a 1972 piece in the Journal of Popular Culture:

The work is no doubt the “biggest all-media parlay in show-business history.” Like the Beatles, though without apology, Superstar is probably more popular than Christ himself. Decca has sold around three million copies of the original album at $10 apiece; the Broadway version hauled in over a million dollars in advance sales; concert touring companies, including some pirates, are picking up a few million on the side; Norman Jewison will be fiddling on some roofs in Jerusalem to film a summer of ’72 version; and-irony of ironies-the original cast of the Broadway show has just cut an album, “a recording of a show that was born from a recording.” One bitter critic expects Superstar sweatshirts and bath salts to come out soon, in a complete “Selling of the Savior.” Even Business Week ran a feature on the profits.

Israel in 4 BC may have had no mass communication, but Superstar definitely exploited every form of mass communication in America in 1971 AD. It was all they talked about, the wonder of the year - something like the Hamilton of 1970-1971, and in fact the soundtrack album was the biggest album of 1971 in the USA.

That amount of prominence naturally leads to enemies:

Many fundamentalist groups are against it. Some zealots calling themselves “Jesus Freaks” even picketed the show opening night in New York, claiming it maligned Christ and Christians-right beside the Anti-Defamation League, which claimed it maligned Jews and Judaism. Superstar seems to have as many enemies as friends on the religious fringes.

The Anti-Defamation League was right to point out that Superstar very clearly blames the crucifixion on the Jewish public, portraying Jewish people as villains singing creepily that 'this Jesus must die', and Pontius Pilate is portrayed as being pushed into the crucifixion by the crowd. However, the main thrust of Huffman's piece is how inoffensive the musical actually is to the broad public who didn't already have heaven on their minds. Huffman, more or less, argues that the appeal was basically to Middle America; the musical is careful to be as theologically unoffensive as possible. Huffman quotes interviews with Webber and Rice where they say that:

Basically the idea of our whole opera was to have Christ seen through the eyes of Judas . . . with Christ as a man, not a god. Our intention was to take no religious stand on the subject, but rather to ask questions. We purposely avoided any reference to Christ’s divinity, choosing to end our story with his death rather than resurrection.

As a result, the musical ends before the resurrection (a depiction of which would have been taking a side; not depicting it allows different people to take different messages from the end of the film). It also doesn't feature any depiction of Mary, mother of Jesus - something that might have offended Protestants or Catholics, depending on how she was portrayed.

Generally, Superstar is associated with the 'Jesus Freaks' movement - i.e., hippies who in their search for spiritual meaning had, instead of going to India and discovering Hare Krishna, went down the road and discovered Christianity. However, Huffman is dismissive of this, thinking that its appeal is more Middle America than that.

He summarises the different responses to the musical at the time:

...young people’s reactions vary a great deal, just as their new votes do: the super-faithful consider Superstar blasphemous and perverted; “others feel it raises the right questions but doesn’t provide any of the answers”; some think it’s fairly good, some think it’s great. Perhaps the only common denominator is that most think it’s worth listening to at least once-which - brings us back to our starting point.

Huffman's take broadly seems in line with a New York Times piece on the controversy when it opened on Broadway:

Unlike Tuesday night's premiere, there were only three or four pickets in front of the theater. The young men, who passed out leaflets criticizing the musical for denying the divinity of Jesus, identified themselves as “Jesus People” or as “Christians.” One of them carried a sign that said “Jesus Lives in My Heart.”

A random sampling of some dozen members of the audience uncovered no one who found the musical offensive on religious grounds.

The New York Times piece also asked representatives of mainstream Christianity about their feelings on the musical:

Dr. William A. Marra, assistant professor of philosophy at Fordham University and vice president of Pro Ecclesia, a conservative Catholic lay organization that picketed the theater Tuesday night, called the musical “blasphemous” and said that it was “asinine that Catholics should permit their adorable Jesus to be blasphemed.” He said it denied that Jesus is truly the Son of God” and pictured Him, rather, as “a mere man with Judas as the star.”

A different Catholic view was expressed by the Rev. James Di Giacomo, adjunct assistant professor of religious education at Fordham University who has written about the musical for religious publications. “Insofar as the musical stops short of the transcendent —that is, that it is not written from the standpoint of faith that Jesus is the appearance of God among men—it is very limited,” he said. On the other hand, the Jesuit believed the musical has real value, particularly for young people, in that “it presents Jesus as a strong, radical leader, attempting to change the world, and not merely from the standpoint of bourgeois religiosity.”

The Council of Churches of the City of New York (a Protestant organisation) seemed to think that discussing the music was useful in getting kids to care about Jesus:

The Rev. D. Dan M. Potter, executive director of the Council of Churches of the City of New York, said that, although his organization would officially not comment, the council had encouraged church and youth groups to use the album of “Jesus Christ Superstar” in study programs. He said Protestant opinion was divided on the religious aspects of the musical.

So, broadly speaking, there was controversy (though I gather in the musical-theatre world, the controversy was more about it being a rock'n'roll opera rather than something more traditional - Huffman mentioned Schonberg refusing to call it music, and that the Broadway producers probably loved the attention and publicity, which does not seem to have affected sales). But the controversy, also broadly speaking, was a controversy between the more conservative and progressive sides of the mainstream Christian Catholic and Protestant traditions, as the musical clearly appealed to the progressives but not the conservatives - rather than simple sheer outrage.