Yeah, that’s the whole issue though, the school receives public funding which makes it much less clear.
A constitutional right should not end if and when you cross state lines, nor when you walk onto a campus.
It is my understand that for private businesses to prohibit guns it must be clearly marked, and that includes banks.
Put it this way…if I’m not going through a metal detector…I don’t like thought of being asked to be unarmed. It’s way too easy for some douche-bag to sneak one in and start shooting fish in a barrel, much like any recent school shooting.