Police will generally enforce private property rights by forcibly removing trespassers (although it sometimes takes a while). The problem is that homeless people usually occupy public property. Police can prevent them from doing certain things like blocking sidewalks but otherwise they have the same legal right to be on public property as anyone else.
Even for occupation of public property, the application of state power is extremely selective. Abandon or live in a beat to shit tent on public property, get arrested and have your private property destroyed by the state. Leave a $50,000 BMW in a bike lane because you're too self important to find a legal parking spot, and at best you'll get a ticket. Most of the time you might not even get that much.
The fact that only one of these will be on the receiving end of state violence really underscores how little the excuse of "you're occupying public property" has with the expected outcome.
