According to an article in The Commentator (link), my judgment (link) on the subject of a transgender professor at YU matched that of R. Hershel Schachter and R. Hershel Billet. The article quotes the two rabbis as follows:
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Rabbi [Hershel] Schachter noted that many of the professors in the university are Jewish and are not observant. "Why is this any different?" Rabbi Schachter asked. Furthermore, there are professors in the college who are homosexual, which has not been a major source of contention for students. "This is an issue every Yeshiva that teaches secular studies has to deal with," said Rabbi Schachter. He felt that YU should not dictate that its faculty hold Torah perspectives. At the same time, he felt that students should be able to take students [professors?] who share their values: "if students want to boycott the course, let them boycott the course."
Rabbi Herschel Billet, rabbi of the Young Israel of Woodmere and former president of the Rabbinical Council of America (RIETS ’75, BRGS ’80), largely agreed with Rabbi Schachter. He said, "SCW, like most Orthodox Jewish schools, never required its secular faculty to be halachically observant." So long as a professor was "respectful of the Orthodox Jewish character of the student body," Rabbi Billet did not feel they should alter this policy – regardless of the sexual orientation of the professor.