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Not all members of the group are Christian, she said, but leaders are expected to set the example with prayer, Bibles studies and worship.

Someone who does not believe in Christian doctrine could not effectively lead those activities, she said.

“We aren’t going to compromise on our core religious identity,” she said.

Vanderbilt officials have defended the nondiscrimination policy by citing a 2010 Supreme Court decision upholding a similar nondiscrimination policy for school-subsidized student clubs at the University of California’s Hastings College of Law.

But Vanderbilt law professor Carol Swain said the administration’s interpretation goes beyond the Supreme Court ruling and is being enforced unfairly.

University officials, she said, have made exceptions for traditional fraternities and sororities while applying the policy to conservative Christian groups not affiliated with a denomination.

Ms. Swain, also an adviser to the Christian Legal Society, one of the Christian groups at odds with the college, said she expects other groups, like Vanderbilt Catholic, will decide to duck the rules and go unsanctioned by the administration.

The clubs have until April 16 to apply.