From Pope John Paul II:
"13. Since the objective of a Catholic University is to assure in an institutional manner a Christian presence in the university world confronting the great problems of society and culture(16), every Catholic University, as Catholic, must have the following essential characteristics:
"1. a Christian inspiration not only of individuals but of the university community as such;
"2. a continuing reflection in the light of the Catholic faith upon the growing treasury of human knowledge, to which it seeks to contribute by its own research;
"3. fidelity to the Christian message as it comes to us through the Church;
“4. an institutional commitment to the service of the people of God and of the human family in their pilgrimage to the transcendent goal which gives meaning to life”(17).
“14. “In the light of these four characteristics, it is evident that besides the teaching, research and services common to all Universities, a Catholic University, by institutional commitment, brings to its task the inspiration and light of the Christian message. In a Catholic University, therefore, Catholic ideals, attitudes and principles penetrate and inform university activities in accordance with the proper nature and autonomy of these activities. In a word, being both a University and Catholic, it must be both a community of scholars representing various branches of human knowledge, and an academic institution in which Catholicism is vitally present and operative”(18).”
From Pope Francis:
The pope called for Catholic institions like Notre Dame to embrace an ethos of “missionary discipleship.”
"Essential in this regard is the uncompromising witness of Catholic universities to the Church's moral teaching, and the defense of her freedom, precisely in and through her institutions, to uphold that teaching as authoritatively proclaimed by the magisterium of her pastors."
Francis also urged Notre Dame to resist efforts to undermine the university’s witness to the faith.
"It is my hope that the University of Notre Dame will continue to offer unambiguous testimony to this aspect of its foundational Catholic identity, especially in the face of efforts, from whatever quarter, to dilute that indispensable witness. And this is important: its identity, as it was intended from the beginning. To defend it, to preserve it and to advance it!"
I hope this provides guidance regarding supporting institutions that provide a diluted witness.