One thing that is distinctive about religiously-affiliated schools is that we very often discriminate in hiring. Specifically, in diverse ways, we favor members of our faith over those who are not a part of that faith. Within our group, we vary from schools that have almost no religious favoritism in hiring to those who hire only from members of the faith (or those willing to live under its strictures). My own school, Baylor, is probably more towards the restrictive end of this continuum-- our University demands a relatively close inspection of a candidate's faith, and our current law faculty contains no non-Christians.
Critics of this type of discrimination properly point out that it limits the viewpoints a student is exposed to, and may restrict the debate within the faculty.
However, those problems are costs which many institutions are willing to bear in order to retain their denominational identity, foster the views professed by the sponsoring faith, and provide diversity to the larger national discussion on legal issues from a place of moral certainty.
What I wonder at times is how intentional all this is-- that is, are we sure we are getting the benefits that would justify the costs?