When it comes to 'Catholic Identity' of any Catholic Institution, we must follow the Principle,  "First, DO NO HARM", to the faith.  That means the Catholic University CANNOT be promoting, supporting or engaged in activities which undermine the established teachings of the church on Faith and Morals.   Consider the hot button of Homosexuality.  The University could have some sort of campus ministry to people who have a homosexual inclination, so that they can understand the Church's clear teachings, and learn to integrate the teachings of the church into their lives.  This ministry to homosexuals could NOT promote homosexual marriage, or an active homosexual lifestyle.  Conversely,   If there were a Business Club on Campus, it would have to absolutely reject the exploitation of peoples at the altar of profit.   So a true Catholic university does NOT fit into 'Liberal' or 'Conservative' camps, but promotes all the truths of the faith, regardless of political alignment.