They don't want to run the risk of the government ever being able to come in and tell them what to do because they accept government money.
I can understand that concern. What the government pays for, they want to control and government control of a religious institution is not acceptable IMHO.
Thats all well and good but has no bearing upon the GI Bill since the funds are available to ex-military and do not control anything.
Students have attended religious schools all over the country on the GI Bill for over half a century and those schools have had no interference from the fedgov as a result. Notre Dame, Loyola, DePaul, Concordia etc. are only a few of the better known.
While I would never go to a school as dimwitted as this or encourage anyone else to. Those who accept such convulted and paranoid reasoning are welcome to attend.