For Ms. Lyon, the question of whether to stop studying the works seemed a no-brainer. But the school’s academic senate rejected the petition in a statement, citing concerns about free speech.

Canceling a course because its materials are controversial or seen as morally problematic, the senate said, “would undermine both the value of free inquiry and the associated rights of faculty to engage in such inquiry by choosing their course content.”

Ms. Lyon was unmoved. “When you teach works like Woody Allen’s you’re normalizing and romanticizing the culture of abuse he was part of,” she said, noting the parallels between accusations against Mr. Allen and the relationships his characters have with younger women in films like “Manhattan.” “It’s not censorship to be selective when you choose the art you teach.”

Educators say that their worries about curriculum changes are more complex than censorship, and wonder whether some perspectives, especially those of authors of color, can be replaced.

Nadia Celis, an associate professor of literature at Bowdoin College, had her “Teaching the Caribbean” class upended when the author Junot Díaz was accused of harassment and unwanted sexual contact with at least two women last year. M.I.T., where Mr. Díaz teaches, cleared him of misconduct after an investigation found no evidence of his wrongdoing, but the accusations prompted intense debate in the literary world.

News reports of the allegations spread the same week Professor Celis’s class was discussing Mr. Díaz’s novel “The Brief Wondrous Life of Oscar Wao.” She had planned for her students to discuss the novel’s themes, including toxic masculinity and abuse of power. Suddenly, she said, it seemed those subjects had come to life.

Her students were disheartened. Professor Celis had previously brought Mr. Díaz to campus to address students on navigating professional success as a man of color. Now she felt torn about using his most famous book — and still has not made up her mind about whether to assign it this year .