Many of New York City’s once-vaunted private schools are hunting for the next generation of woke educators to preach the gospel of anti-racism and critical race theory, a review of job applications by The Post shows. Leading the way is Ethical Culture Fieldston School, which is on the market for a ballet instructor “committed to challenging Western dance forms and the hierarchical and pedagogical practices that often center whiteness in dance classrooms and on stages,” according to a job description posted to the school’s website. Even science at Fieldston — a Bronx institution where tuition is $55,510 a year — has not been spared the progressive mandate. A posting seeking an upper school biology teacher said applicants should have “an understanding of and commitment to cultural competency, and how to support a diverse student population, especially through teaching more inclusive science curricula.”