It's interesting that these colleges are investigating these groups so carefully. They want to know exactly what you believe, and if you don't believe what they believe, then you get bounced.
Somewhat Orwellian, but maybe it's because they are bound to give funding to these groups if they give them a charter.
My guess is, if they had left the requirement that all officers and members be Christian out of their constitution, they would have had no problem. I assume that they put it there on purpose to pick a fight.