Some private universities have got away with this nonsense but UNC is a public university and therefore subject to the 1st Amendment. They are going to have to back down
"The University of North Carolina-Greensboro has ordered a Christian club to allow non-Christians as leaders and members, according to a federal lawsuit filed Wednesday. “The university has given itself the authority to determine whether a group is religious or not,” said Jeremy Tedesco, an attorney with the Alliance Defense Fund.
Tedesco filed suit on behalf of “Make Up Your Own Mind,” a Christian club that was denied an exemption from the university’s nondiscrimination policy.
UNC-Greensboro’s nondiscrimination policy includes an exemption for student organizations that select their members based on a shared set of beliefs.
Tedesco said “Make Up Your Own Mind” has a clear religious mission and purpose and requires its members and leaders to agree with its statement of faith and beliefs about the value of innocent human life.
“Saying that a Christian club isn’t religious is flatly absurd, especially when the university has granted its belief-based exception to numerous other clubs,” he said. “The First Amendment forbids the government from determining what is and what is not ‘religious,’ yet the university is doing exactly this by telling a Christian group that it is not religious.”
However, the university contends that the club is not affiliated with a church – and therefore doesn’t meet their criteria for exemption.