But the show has made it clear that Mr. Ramasar is staying.

“There is zero consideration being given to his potentially being terminated from this workplace,” it said in a statement last week.

In the run-up to the show’s opening on Thursday, the protesters have proven to be a mild but persistent irritant for the production, a reinterpretation of the classic musical with a modern flair.

This cast is populated largely by young people of color. The director, Ivo van Hove, is known for his experimental work. Mini dresses have replaced full skirts. Smartphones are whipped out to record police abuses.

And the #MeToo-era demonstrations outside are also similarly and strikingly of the moment, as they reflect the continuing debate over what sort of careers should be left to the men accused of sexual misconduct.

Should they be allowed to flourish in new roles? Is there a waiting period during which they must remain in the shadows? Since #MeToo prompted a cultural reckoning, men like Louis C.K. and Aziz Ansari have begun to re-establish their professional lives, while other public figures accused of more severe acts have seen their prospects buried — likely for good.