Nobody reaches for the smelling salts when a college is accused of failing to have enough African-American, Latino, Native American, or female professors. But the University of Notre Dame is now embroiled in a growing dispute over whether it is hiring enough Catholics.

Catholic universities in the United States have a “Potemkin village” quality, writes Rev. Wilson D. Miscamble, a Notre Dame historian. With their crucifixes and chapels, they look like religious institutions from the outside, but inside the classrooms, students learn the same secular lessons they do in other universities. Notre Dame’s faculty was barely 53 percent Catholic in 2006, and a spate of Catholic retirements is coming. The history department, with 32 members, has only 12 Catholics, and when three new hires were made last year, only one was Catholic.