Nearly 30 years ago, a famous soprano told me privately that Plácido Domingo was “a bit of a groper”. She herself had been the object of the tenor’s unwanted sexual attentions during a car journey, she told me. Unwanted but not, it seems, unwonted. In the world of opera, she added, Domingo’s habit was well-known and not unique.

The soprano was a woman who could take care of herself. She told me about Domingo almost in passing and certainly not for quotation or because she thought the story should become public. It was private information. I have never written anything about it until now. But times have changed, and rightly so. Whether the opera world has changed with it is another question.

This week, the Associated Press reported that eight singers and a dancer have said that Domingo sexually harassed them in various incidents since the 1980s. Some of the incidents took place while the women were working in opera houses where the singer was in management positions. That means in either Washington DC or Los Angeles or both, since Domingo, now aged 78, had long management associations with each, a continuing one in the case of the Los Angeles Opera.

Thanks to the impact of the #MeToo movement and the fall of powerful and serial sexual predators such as the film producer Harvey Weinstein, allegations of this kind, like the ones I heard all those years ago, are no longer kept private. In Domingo’s case, this meant that some US opera houses and concert halls have been quick to terminate planned events in which Domingo was scheduled to perform. The Philadelphia Orchestra and San Francisco Opera are among the venues that have rescinded their plans. LA Opera has promised an independent investigation of the allegations.

Others, though, have been more cautious. Domingo is still scheduled to sing at the Metropolitan Opera in New York in September and October, before returning again in November. The Met has said it will await the LA Opera review before deciding whether to continue with the engagements. In Europe, the Salzburg festival, where Domingo is due to perform on 25 August, has had no such scruples. Domingo will perform as scheduled, it has announced.

In the UK, Domingo has had a long association with the Royal Opera House, Covent Garden. His next performances there are not due until June 2020, when he will be seven months shy of his 80th birthday. Even so, Covent Garden is now in the spotlight, too. So are several other European opera houses where he is due to appear over the next 12 months, including Zurich, Vienna, La Scala Milan, Madrid, Hamburg, Munich and Berlin. All of them need to recognise that these allegations have put them on the spot and that they need to put the rights of their employees not be harassed ahead of their loyalty towards a once great artist who is not above the law.

You might think that every one of the houses where Domingo is currently scheduled to perform would at least put their commitments on hold, pending the LA inquiry. Not so. Most seem to be keeping quiet in the hope the storm will blow away. The Salzburg response suggests that they remain reluctant to treat the issue properly for fear of damaging the goose that still lays their golden eggs. “I have known Plácido Domingo for more than 25 years,” the festival’s president, Helga Rabl-Stadler, said in a statement. “In addition to his artistic competence, I was impressed from the very beginning by his appreciative treatment of all festival employees … Had the accusations against him been voiced inside the Festspielhaus in Salzburg, I am sure I would have heard of it … Artistic Director Markus Hinterhäuser, Executive Director Lukas Crepaz and I all agree that Plácido Domingo should perform as planned.”

Domingo in Simon Boccanegra at London’s Royal Opera House in 2010. Photograph: Tristram Kenton/the Guardian

The opera houses are cautious, perhaps culpably and irresponsibly so in some cases, because, in the end, they are caught in a trap that is largely of their own making. Opera houses, especially the biggest ones, rely on stars. Few stars are more lustrous than Domingo. He is the most famous singer in the world. Audiences love him. Opera houses charge top prices for his performances. Sponsors, on whom most opera houses depend, love nothing more than a Domingo evening.

The consequence has been that he has been indulged on purely artistic grounds to a degree that few other performers would ever seek – let alone be encouraged – to emulate. He was once, and for a glorious period, the most outstanding operatic artist of his era. His performances of Verdi’s Otello at Covent Garden in 1980, 1987 and 1990, each time under the baton of Carlos Kleiber, remain the supreme experiences of my own opera-going life. But, at his age, the voice, the artistry and certainly the stage presence are shadows of what they once were. For the past decade, Domingo has toured the world singing baritone roles rather than the tenor roles that he made his own for so long. Yet he is not a true baritone. He should have retired long ago. He is, however, Plácido Domingo, and for many, that has always been enough. But surely not any longer.