Don’t get your hopes up....
“The First Amendment protects this right by prohibiting Congress from making laws that would curtail freedom of speech.”
Key word is Congress. If the SCOTUS say yes to speech police, then every institution or even business can follow.
Be a decision to watch for
Congress is funding every university by guaranteeing student loans, providing grant money to various departments etc....
If the university bans free speech it is acting as an agent of Congress in doing so.