Stanford's "Warning" about Religion

In the course of looking into something having nothing to do with law-and-religion, I came across a web page, provided by Stanford University's Office for Religious Life, entitled "A Word of Warning."  Here is the text:

A Word of Warning

Maintaining and nurturing your spiritual life during college and graduate school is one of the best ways to keep perspective on your studies and to avoid the isolation that is too often a part of scholarly pursuits.  The Deans for Religious Life and members of SAR are committed to providing opportunities for spiritual growth, rewarding friendships and intellectual inquiry into matters of faith in a supportive environment.

Unfortunately, not every religious group has your best interests at heart. Groups to avoid have some or all of the following characteristics.

• Pressure and Deception: They use high-pressure recruitment tactics or are not up-front about their motives when they first approach you. SAR members are required to identify themselves on all News and Publications and to be clear and forthright about their motives.
• Totalitarian Worldview: They do not encourage critical, independent thinking. The first goal of higher education is to enable you to think for yourself. Be aware of groups or leaders who try to control your life or who claim to possess the truth exclusively.
• Alienation: They want to choose your friends for you. While all religions have moral guidelines, watch out for groups that encourage you to sever ties with close friends and family who are not members. They are manipulative and extremely dangerous.
• Exploitation: They make unrealistic demands regarding your time and/or money. If participation in a group takes away from your study time, beware. A group or leader that cares about you understands that your studies-your future-are your first priority as a Stanford student. SAR members are strictly forbidden to require dues from student participants.

If you feel you are being pursued aggressively or manipulated by a group or leader, contact any of the Deans for Religious Life or call 723-1762.

Now, it strikes me as reasonable and appropriate for a private university to provide (perhaps) paternalistic guidance to students on all sorts of matters involving their "personal" lives, including involvement with religious groups and activities.  (I would hope that a University's willingness to provide "warning[s]" to students about the dangers posed by some religions to "critical, independent thinking" would indicate a willingness to warn about similar dangers posed by, say, political or identity-related groups).  I imagine that reasonable people will disagree about what, exactly, "counts" as "claim[ing] to possess the truth exclusively", or "[dis]courag[ing] critical, independent thinking," or a "totalitarian worldview", but put all that aside.

I wonder, would (or should) the First Amendment constrain the issuance by a state-run university of a "warning" like Stanford's?  Or, approaching the matter from a broader, "religion and liberal democracy" perspective, or from a "Catholic legal theory" perspective, what should we think about this "warning"?

Rick