I think this is an issue of terminology that is specific to discussion of colleges and universities. Generally, in this context, "Christian" and "Catholic" are distinctly separate. Illustrating the point on this, many Catholic elementary and secondary schools are emphasizing this point by returning to their roots ... "XYZ Christian High School" becomes "XYZ Catholic HS"
But it is not an intent to malign or pass judgement on the faithfulness of Catholicism. To the contrary, last I noted, Christ is front and center; yesterday, today, tomorrow for Catholics and Protestants. Purist theologians may debate the issues of Mary, the cup, and others, but the final judgement of that might best be left to the Final Judge.
RE: Catholic/Christian colleges desiring/welcoming non-Believers, they vary widely. Some see the higher education process as a deeper indoctrination, study, and engagement of a prior commitment. Others see the process as one in which non-Believers may be exposed to both doctrinal issues, materials, and learning as well as developing relationships with believing Christians. In other words some see the campus as a potential hotbed for implementing the Great Commission while others may view it as training for such, but do not wish to encourage or nurture a wide-open debate. For those considering Christian or Catholic schools, exploring this aspect of the institutional mission is critical, it seems to me.