No, I have no problem with that. I'd likewise have no problem with the university sanctioning a Catholic Club that made allegiance to Pope Benedict XVI a requirement for membership.
I'd simply object to a "Christian" club making allegiance to the WCF a requirement for membership, for the same reasons you'd object to a "Christian" club that made allegiance to Pope Benedict XVI a requirement for membership.
Actually I wouldn't object. First come first served on the claim to the the "Christian" club. If the Catholics didn't claim it first, then they would have to start a "Catholic" club.
The whole idea of a "Club" is to have a creed or common interest that the members are dedicated to. I suppose we could limit the membership to those who were in agreement with the Apostles Creed or the Nicene Creed and this would open it up to both Catholics and Traditional Protestants. But the Mormons and Jehovah's witnesses would object. Do you really care if they objected?
The problem we have in this society is that we are not willing to promote individuality and to discriminate on the basis of beliefs. The Universities want everyone to be part of the collective and therefore nobody can be excluded from membership in any club merely because they disagree with everything about it.
You start your "Christian Club" and make agreement with the Catholic Catechism a requirement for membership. Great, more power to you. I'll start a different club with a different creed. That's the American way.