LOS ANGELES — It seemed like routine business for the student council at the University of California, Los Angeles: confirming the nomination of Rachel Beyda, a second-year economics major who wants to be a lawyer someday, to the council’s Judicial Board.

Until it came time for questions.

“Given that you are a Jewish student and very active in the Jewish community,” Fabienne Roth, a member of the Undergraduate Students Association Council, began, looking at Ms. Beyda at the other end of the room, “how do you see yourself being able to maintain an unbiased view?”

For the next 40 minutes, after Ms. Beyda was dispatched from the room, the council tangled in a debate about whether her faith and affiliation with Jewish organizations, including her sorority and Hillel, a popular student group, meant she would be biased in dealing with sensitive governance questions that come before the board, which is the campus equivalent of the Supreme Court.

The discussion, recorded in written minutes and captured on video, seemed to echo the kind of questions, prejudices and tropes — particularly about divided loyalties — that have plagued Jews across the globe for centuries, students and Jewish leaders said.