Actually, it's a bit different in California. There was a case at the state Supreme Court that ruled that, basically (IIRC, and IANAL) free speech rights still apply on private property as long as that property is open to the public and as long as you're not disrupting business. (I think the court case involved a union handing out leaflets; even though they were more or less trying to convince people not to shop at a particular store in the mall, the ruling was that as long as they didn't create a disturbance or block access to stores, they were within their rights.)

Commercial behavior could be regulated, as could (one would assume) anything that disrupted business or monopolized the space...but a group of people showing up in interesting outfits to patronize one of the attractions in the mall would seem (again, IANAL) to be less of a borderline case than the union info campaign that was ruled an exercise of free speech.