“It was kind of gross how easy it was to be able to say, ‘This person has to be this,’ ” said Camille Fillion-Raff, a junior at the school.

Educators who do this work in New York private schools say one of the challenges white students face when exploring their own identity is the dearth of white anti-racist role models. They say white students have traditionally been offered only three ways to confront race: to be colorblind, ignorant or racist.

“Those are not happy identities,” said Beverly Daniel Tatum, the president of Spelman College and the author of “Why Are All the Black Kids Sitting Together in the Cafeteria?”

With that in mind, the Trevor Day School on East 89th Street spends at least some time every year honoring the white civil rights activist Andrew Goodman, who was killed in Philadelphia, Miss., in 1964, while working to register black voters. This year, the school invited Mr. Goodman’s brother, David, to speak at the school.

But helping students explore their white identity has not been without its challenges.

At the Ethical Culture Fieldston School, which has campuses in Manhattan and the Bronx, a plan this winter to roll out a racial awareness workshop series for third through fifth graders was met with fierce resistance by parents. Many objected that children as young as 8 were being asked to segregate themselves into race-based affinity groups. Ultimately, parents were told, students who chose not to identify with any of the racial categories would be allowed to sign up for a group that was not based on race. A fifth grader’s father, a white man who asked not to be identified because he did not want any repercussions for his daughter, called the plan “mind-boggling” and said his daughter found the entire concept confusing and unsettling.

At Brooklyn Friends, a controversy over the approach of Dr. Moore, the school’s former diversity director, ended abruptly when he left at the end of last year and did not return this fall. Many students, like Jumoke McDuffie-Thurmond, a black senior, said Dr. Moore was a warm and stimulating figure at the school who talked openly about what he called “subconscious racial bias.” But several sources inside the school said some white students complained that Dr. Moore was a polarizing figure whose focus on white privilege made them uncomfortable. Both Dr. Moore and a school representative described his departure as “amicable.”

At LREI, Sandra Chapman, the director of diversity and community, said conversations about white privilege could be difficult, with some students and faculty members more willing to engage than others. “This is messy work,” she said. “But these conversations are necessary.”