So if that were actually the requirement to join one of the Christian Clubs at Vanderbilt, would you support the University if they prevented the club from making that a requirement of membership?
It would be no different than requiring people to sign an oath that they believe in the Book of Mormon in order to join the "Christian Club". That's not "Christian", it's LDS. No one would agree to do so unless they're members of the Church of Jesus Christ of Latter-Day Saints. And no one is going to pledge support for the Westminster Confession unless they're Calvinists.
Fortuntantely, I can't think of any "Christian club" at any university that has such a requirement. I have no problem with the club requiring members accept Jesus Christ as their as Lord and savior. EVERY practicing Christian does that.