re: LSU having to deal with a “free speech” versus “hate speech” issue

LSU is a public university governed fully by the First Amendment. As a government body, LSU cannot sanction a student, faculty member, or other employee for expression that is protected by the First Amendment. There is no hate speech exception to the First Amendment, so while the expression referred to in the original post is deeply offensive and hateful, it is fully protected. The student is fully entitled to the admission that has been granted by the university.

That doesn't mean that people cannot express their own views about his expression and stand in opposition to what he said. Individuals should not be subject to harassment, but those who object to what was said also have a right to free expression and can state that they object.