With a few exceptions, the owner of the private property retains control of the the property as being private property. That owner can stop the carry of guns onto the property (2nd Amendment). That owner can stop somebody from setting up a printing press, using the property for church services, or engaging in public speaking, such as a politician who might want to use the property for a backdrop to further a campaign talking point (first amendment). Trespass laws are still in effect. The exceptions tend to be issues related to sex, race, and religion (of the person), and in some cases, gender preference.