Here is a thoughtful and, in my view, accurate answer to the question. by Michael Bradley on the Ethika Politika blog (HT my eldest). He first determines that, according to a couple of criteria taken from Ex Corde Ecclesiae, ND is failing even its own criteria for being Catholic, esp. in the area of percentage of faculty who embrace the Catholic intellectual tradition. He then makes the following point, which I have seen with my own three children who have gone to ND.
But a more practical question on the minds and hearts of many American Catholics is where they can send their children to receive a viable, robust, fruitful Catholic education, a tertiary schooling experience from which students can emerge as Catholic adults prepared to live as vibrant witnesses to the world in service to the Church. I submit that Notre Dame belongs in every responsible answer to that query, and that the Catholic educational experience on offer at Notre Dame is among the very best in America. One just has to be intentional—and perhaps lucky—to experience it.I guess the best way to put it is that there is a Catholic university experience available at Notre Dame, but that it is mixed in with a University (community of scholars) that has a different logic. Institutionally, the battle rages, but for the student who pursues it, there is a real, vibrant Catholic intellectual, cultural and spiritual tradition. Unfortunately, most students there don't know they ought to pursue it.