"Open to the public" considerations in trespass is generally a concept applying to commercial property. If you allow passage for all, you can't restrict it arbitrarily. No kids, no black people...you can't charge people with trespass if the property is generally open to the public (speaking of a mall rather than a bar with legal restrictions). My apartment building is not open to the public, though I suppose the sticking point is that my porch is, absent signage or other fence-y stuff.

| If you allow passage for all, you can't restrict it arbitrarily.

I know more about private property in regards to the 4th Amendment, but in those situations anything that is accessible to the public, like a walkway to your front door, driveway, etc those are all legally permissible areas for a police officer to be, even though they haven't been invited onto your property. I'd imagine they'd make a similar argument that you can't have a part of your property open to the public but then only restrict people passing out phonebooks/flyers/etc.