It’s not a question of CMC’s ability to curtail access to someone’s “speech”, but of the students and others ability to come to campus and interfere with others ability to “peaceably assemble”.
Clearly the first amendment includes not only the right to free speech, but also to peaceably assemble. There is a right to “hear someone speak”.
CMC being private or public, has nothing to do with this, the same issues would have been raised if the speech was at UCLA.