Ms. Johnson said that she had felt the impact in her own career. “I’m often defined by my cultural background, instead of by my individual skills and qualities,” she said.

One bit of data is especially striking: Stage managers, who assist directors as shows are rehearsed and then manage them on a daily basis once the runs begin, are overwhelmingly white. Only 6 of 137 stage management jobs for Broadway and touring productions went to African-Americans during the years studied, Equity said, and only 5 of 226 Off Broadway.

“It’s a hard business to break into,” said Winnie Y. Lok, who has worked as a stage manager on four Broadway shows (including “Venus in Fur”) as well as a number of shows Off Broadway and in Los Angeles. “Producers and general managers are used to hiring the same people for comfort, and that’s an issue when you’re talking about bringing new people into the fold.”

Ms. Lok said that she never felt her Asian-American background was an issue when competing for jobs, but she was often aware of her gender. “Especially on Broadway, it was a boys’ club,” she said.

In recent years, concern has been expressed about the paucity of commercial productions of plays and musicals by women and minorities, and about the lack of representation of women and minorities in many backstage jobs. There have been many studies of different sectors of the industry, and a variety of efforts to address different aspects of the issue — the Theater Development Fund has begun working to try to diversify theater box offices by starting an apprenticeship program at the TKTS booths; Roundabout Theater Company has started a new fellowship program for a variety of backstage jobs; and a Los Angeles-based collective called the Kilroys, trying to help diversify the array of work presented on American stages, has just released a list of recommended new plays by female and transgender writers of color.

Equity recently hired Nicole S. Smart as its first diversity director. The union’s executive director, Mary McColl, said that Equity would try to diversify its own organization and to start meeting with producers, writers, directors, designers and choreographers to discuss challenges facing the industry. Equity’s British counterpart has been making a similar push.

“I think it’s because the canon is written with more characters for men, and all of us have to sit down and have hard conversations about how to address the problem,” Ms. McColl said. “And if people of color can’t see themselves onstage, how long will theater remain relevant? This is one of the big problems facing the industry, and we want to help solve it.”