“To be fair, the First Amendment says nothing about state/local governments, privately owned businesses, or even the executive or judicial branched — it applies specifically and explicitly to the Congress.”
You are very off base. The first amendment does not only apply to congress. Where did you get such an interpretation? The body of law arising out of the 14th amendment has indeed made the states subject to the 1st amendment.
For about the last 100 years the bill of rights has been applied to the states. Also, this “private” institution is probably taking all kinds of federal money. That comes with strings. Free speech zones won’t stand. Also, the justice department is no longer the friend of such radicalism as free speech zones.
PS: Pierce College is one of the Los Angeles Community Colleges (a public school).
FYI.