There is a common misconception that facilities that allow public acces are 'public spaces'. This has led to many ill-conceived property right infringements. Smoking bans are the most recent example (volokh.com). As more and more behavior becomes stigmatized or as other political trends come to light, this fundamental misunderstanding will become yet another tool to regulate and control.
The misconception has a very obvious origin. A place that any person is generally allowed to enter without being screened in some other way is considered 'open to the public'. Most retail stores, doctor's offices, and real estate offices would be examples. Once a location becomes 'open to the public' it is easy to conflate the terms 'open to the public' with 'public space.' A 'public space' has the very specific connotation of belonging, in some way, to the populace. Most parks, government facilities, public schools and roadways are considered public spaces. A public space is usually 'open to the public.' That both types of facilities are 'open to the public' does not make them both 'public spaces.' True 'public spaces' are wholly owned by the government. The other facilities that allow public access are privately owned by individuals, corporations or other cooperative groups. These are private buildings and businesses.
That 'public spaces' belong to th government, it is often assumed they belong to the people since the government is 'of the people.' The logic, it seems, dictates that 'public spaces' are for everyone in the public and because the government belongs to the people, thus every person has a right to use the space. It is this new right that seems to allow the most harm when combined with the wrong understanding of 'public access.' Once an entity allows public access and is misconstrued to be a 'public space' now it is assumed every person has a right to use that facility or space. This is, of course, sloppy thinking at its most dangerous. Treading on property rights of any entity is harmful to property rights in toto.