[R]acist speech is constitutionally protected, just as is expression of other contemptible ideas; and universities may not discipline students based on their speech. That has been the unanimous view of courts that have considered campus speech codes and other campus speech restrictions — see here for some citations.
I believe that both men are, in context, talking about public universities rather than private ones. Here’s what the Foundation for Individual Rights in Education says about the latter:
Unlike public universities, which are of course government actors, private universities are not legally obligated to uphold the First Amendment rights of students on campus. In fact, private universities have a First Amendment freedom of assembly right to determine for themselves the terms of matriculation, within certain legal limits. However, many-in fact, most-private colleges and universities advertise themselves as bastions of free and liberal learning, where all viewpoints can be expressed, discussed, and debated. Most private universities promise their students extensive speech rights in school materials such as student handbooks, recruiting brochures, and codes of conduct.
When a school, public or private, makes a promise to a student–whether in a student handbook or a brochure or a speech from the president-that school is morally and legally bound to honor that promise. Courts have held in several cases that private institutions must live up to these types of promises, based on a “contract theory.” . . .
As a private entity with its own institutional First Amendment rights, a private college may choose to define itself as being committed to values other than free speech, as long as the school makes it publicly and consistently clear that it holds a certain set of values above a commitment to free speech. For example, Brigham Young University (BYU) is quite forthright in its stated policies that students entering BYU are not guaranteed robust free speech rights. . . . If a private college clearly does not promise free speech, and the college makes this known publicly and consistently, entering students have given informed consent and have voluntarily chosen to limit their own rights–in much the same way students entering military academies or theological seminaries understand that they are relinquishing many rights they would enjoy at a state college.
That is how the law treats private colleges and universities, according to FIRE; and in my view it’s a good thing the law treats them that way.