pdq is right about his observations being in California under California law. New Jersey, Colorado, and North Dakota- maybe a couple of others - are with them. Most are not. Alaska has not addressed it. The analysis works in a counter-intuitive direction: If a state like California wants to protect free speech in quasi-public areas (i.e malls and on private university campuses), the federal courts can knock them back IF the State is unreasonably infringing on property rights. (Land leased from the State or otherwise having some sort of state "presence" may also be subjected to tougher standards favoring free speech.) California does it its way at malls, and New Jersey added in private university campuses, but most states don't bother.

(The feds used to lean toward the freedom of speech side, but tilted toward private property rights in 1976 ("Hudgeons.") pdq's case is "Pruneyard," 1980.)