You never had a right to establish any shelter. You have a right to appropriate what's unowned or receive something in voluntary exchange.

Now if you stand on a justly owned property (like my house), then you play by the rules of the owner or go away.

If you stand on unjustly owned property (like a forest protected by the state), then you may use part of it as your own provided you do not alter objective properties of this forest that were enjoyed by everybody prior to you. E.g. if you noticeably alter the air quality by cutting it down, prior users of the air may ask you for compensation.

Also, it's a losing strategy to talk about somebody's obligations. If somebody has robbed you, he must 1) compensate what's stolen 2) be punished. He is not obliged to provide you with social security, free speech and fast internet.

While there is some marginal amount of class mobility, property ownership in the U.S. is correlated almost entirely with privilege. The more white/rich/male/citizen/straight/cis/typical-bodied/neurotypical boxes you can tick, the more likely you are to be a property owner.

The fact that you think Mitt Romney owning property is "just ownership" while the children of, say, a non-citizen Native American who came back across the Mexican border in the 90s to his ancestral lands in San Diego county are "just non-property owners" is absurd.