A few things:

Free speech is not a universal right. There are clear exceptions especially for school-registered organizations (up to and including the promotion of illegal activities). The constitutional rights of students in public school are not automatically coextensive with the rights of adults in other settings (see: New Jersey vs T.L.O.). This was affirmed in Bethel School District vs Fraser: " In upholding the students' right to engage in a nondisruptive, passive expression of a political viewpoint in Tinker, this Court was careful to note that the case did 'not concern speech or action that intrudes upon the work of the schools or the rights of other students.'" The Tinker Test doesn't apply in this instance because Tinker only held that political speech which was not disruptive is protected (the case example being a few students who wore black armbands to protest the Vietnam War). Racist threats of lynching are not political speech and are certainly disruptive to the safe and secure educational environment for black students on campus.

The link you provided is nowhere near conclusive and contains many arguments that support regulations. For example, it only cites cases of stereotypical speech as being universally protected. By contrast, citing Virginia v. Black, the article concedes that speech with a "long and pernicious history as a signal of impending violence" can be regulated and punished. Threatening to lynch black people obviously meets this standard, regardless of whether they actually intended to carry out such a threat.

What's most important to note is that the students aren't being expelled for simply being racists (which is messed up but obviously protected). The students are being expelled for creating a threatening environment through the promotion of an historically racist, violent action (lynching).

Simply saying the words "free speech" is not a legal argument nor is it a universal standard.