I see. Using an institution's mission statement would seem as good a method as any to designate the net purpose of an institution which is in reality manifold. I wonder what is in fact currently the measure? Also, it would be interesting to pursue another aspect of this further: in what way is the (non-state) university receiving federal money? Are you speaking solely of student financial aid money, or are there other matters? And isn't it technically the student which receives aid? I realize that this is a technicality and a simplification which might well be described differently. But upon such technicalities is policy built.

In this case, the new big question would be this: what determines the set of institutions for which students may be aided financially? An Islamic institute should surely qualify if a Christian one does. However, even within Christian colleges, there is a divide between colleges and seminaries or "Bible colleges," i.e., schools which instruct only or mainly on matters of religion and theology.

Here, as in the wider question of how to differentiate between schools of varying caliber and purpose, accreditation seems perhaps the best method. But I'm well out of my depth regarding what the standards in fact are.