I’m not so sure about this - my understanding is that in some states a private venue cannot ban weapons on the premises with the reasoning being that such a ban would violate the individual right to bear arms. I’m not if this is the case in Utah but it seems to be; in Utah churches, for instance, are explicitly allowed to ban weapons but only if they file that notice with the state annually. Presumably without that explicit exemption in state law, private businesses cannot ban firearms.
EDIT: Actually, it would seem that carrying on a Utah campus is explicitly permitted under law, as it is in six other states, so there’s no way to ban guns from a venue. At least that’s how I read it.