(Reuters) - A university can legally deny recognition to a Christian student group that bars gays and nonbelievers, the U.S. Supreme Court ruled on Monday in a case that pitted anti-discrimination principles against religious freedom.

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Such official recognition qualifies campus groups for funding and other benefits.

By a 5-4 vote, the justices upheld a U.S. appeals court ruling in favor of the University of California's Hastings College of the Law. It denied recognition to the group because of a school policy that membership should be open to all.

The high court's ruling was a defeat for the Christian Legal Society. It argued the U.S. Constitution does not allow a school to deny recognition to a religious student group which insists its members agree with its core views.

The group requires members to sign a statement of faith that vows devotion to Jesus Christ. It bars those with what it defines as a "sexually immoral lifestyle," including gays and lesbians.

Founded in 1961, the Christian Legal Society has law student chapters across the country. Its members hold Bible study meetings and discuss ways to apply their religious faith to the practice of law.

The Hastings College of the Law chapter initially was open to all students, but in 2004 began requiring members to endorse a statement of faith and barred anyone who engaged in "unrepentant sexual conduct."

The state-run law school in San Francisco cited its anti-discrimination policy and withdrew official recognition, though it allowed the group to continue to meet on campus.

The school said official campus groups may not exclude people because of religious belief, sexual orientation or other reasons.

A federal judge and then a U.S. appeals court ruled for the law school, holding that its policy was reasonable and that it did not violate the rights of the Christian group.

The Supreme Court, in a majority opinion written by Justice Ruth Bader Ginsburg, agreed.

Summarizing the ruling from the bench on the last day of the court's term, Ginsburg upheld the university' open-access policy and said other law schools have similar policies.

She said the university need not provide a religious-based exception to its policy that groups must open membership to all students who want to join.

Chief Justice John Roberts and Justices Antonin Scalia, Clarence Thomas and Samuel Alito dissented.

The Supreme Court case is Christian Legal Society v. Martinez, 08-1371.

(Editing by Alan Elsner)