“Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.”
Per the clear language of the 1st Amendment, there is no abridgement of the 1st Amendment rights of the students. They were free to use any language they wanted, the National Organization of SAE was free to shut down the chapter. The 1st Amendment protects speech from (federal) government sanction. It doesn’t protect individuals from the consequences of saying stupid things.
SAE, as a private organization, had every right to sanction those racist twerps.
Similarly, if OU were a private university it would have every right to sanction those racist twerps.
However OU, as a public university, operates under much stricter constraints, including the 1st Amendment. Sanctioning those racist twerps qualifies as governmental action. Case law and precedent are clear on that.