Daniel Barenboim, one of the world’s most celebrated conductors, is known for doing what he wants.

He founded an orchestra (the West-Eastern Divan, a youth ensemble of musicians from around the Middle East), a conservatory (the Barenboim-Said Akademie) and a concert hall (the Pierre Boulez Saal). In 2001, he broke a longstanding informal ban in Israel and conducted a piece by Richard Wagner, an anti-Semite beloved of the Nazis. He makes the kind of political statements most musicians avoid.

Mr. Barenboim, 76, has long been considered untouchable in Berlin, where he is music director of the Staatsoper — the city’s premier opera house — and principal conductor for life of its orchestra, the Staatskapelle. He is close to city politicians and has used his influence to ensure the opera company receives a healthy annual subsidy of 50.4 million euros ($57.4 million) from Berlin’s government.

But cracks have begun to emerge in the conductor’s image as Mr. Barenboim has been accused of bullying and humiliating members of the Staatskapelle. The accusations have been reported widely in German media, and there have been calls for politicians to intervene. A spokesman for Klaus Lederer, Berlin’s highest-ranking official for culture, whose department provides most of the Staatsoper’s funding, said Mr. Lederer has asked the opera company to appoint a third party to look into the matter.

“A piece of art might not always be democratic, but a public institution can’t be allowed to transform into a royal court,” said a recent article in the newspaper Der Tagesspiegel.