"The institution of private property, in the full, legal meaning of the term, was brought into existence only by capitalism" - Ayn RandObjectivist "Anarcho-Capitalists" who think of themselves as "more Rand than Rand", usually see Ayn Rand's flawed critique of anarchy and support of minarchy as inconsistent and probably think of her rejection of polycentric law as just her having a "mental barrier to entry" so to speak. This quote suggests otherwise. I think it suggests (correctly) that private property is an institution, a legal right that society needs to respect, and that there must be a legal monopoly enforcing it, so that all recognize it.
Because, in a minarchy, people are forced to recognize the legal privilege of private property. That is, if a corporation builds a factory near your community and is given the legal right to dump toxic waste in the lake nearby, you can protest all you like, but you are still forced to recognize the corporations right to own and use that factory, and your tax money is used to protect that legal institution.
But it's different in a stateless society, or, in a contract law society. A contract law society is a society in which law isn't created by state coercion, but by voluntary agreement. Contracts would be made between actors, and enforced by Dispute Resolution Organizations.* Much has already been said about how absentee ownership and private control of means of production might decrease because of increased cost of insurance and protection and other things under such a society, and that mutualist practices and rights would be more practical and desirable in such a situation. But another thing that we should keep in mind is, that nobody is forced to recognize private property.
Let's say Klaus wants to build a factory and claim private control over it. He lives in a contract law society. Klaus needs a few legal privileges in order for him to have an incentive to build it in the first place. First of all, Klaus needs protection while he's homesteading the land and building the factory, so that nobody steals or destroys the things he is building with. He will also need insurance, so that he can be compensated if that happens. When the factory is built, he'll need a contract with an arbitration agency fully protecting his new factory, as well as insurance for the now built property.
Now lets say that the communities that are close to were Klaus wants to build his factory are aren't very happy about what Klaus is doing. They are worried that Klaus's factory is going to use up too much land and natural resources, and thus create more scarcity, and weaken the economic position of all other buyers and sellers of goods, or communes and self-reliant communities for that matter. They are worried he'll pollute the environment and/or dump toxic waste the lake. They are worried that the workers he seeks to employ will be treated poorly. What can they do?
It's fairly simple. They can firstly, create a voluntary organization and network of people who are opposed to such contracts, and discuss ways of undermining them together, by boycott and other things. They can demand secondly, the right of knowing what contracts their Dispute Resolution Organization (DRO) sign. They could demand that the legal contracts and insurances related to property titles are official to all of the customers of the DRO. If these contracts are not made official, they will simply stop associating with the DRO and find another one that does. The demand will most likely be met, since losing that many customers would be harmful. 3rd, in a contract law society, people will not interact with someone who does not have a legal contract with a DRO, or legal protection of his property. If Klaus did not provide legal documentation to workers for the factory they work in, they would not associate with him, mainly because they wouldn't have any legal protection if something happens to them. Also, if Klaus cannot provide legal documentation to the people he is trying to sell his goods too, it is not likely that they will buy his products.
4th, Even if a contract is made with a DRO, even that still does not mean that the contract will be respected. If a DRO does recognize Klaus's right to his factory, the people opposed to it will join other DRO's and demand that they do not interact with the DRO that created Klaus's contracts. The DRO's protection of Klaus' rights to his factory thus become meaningless, since the DRO now can't interact with other DRO's and create contracts with them, which is one of the main functions of a DRO. Contract Law is a system of collaboration rather than a system of coercion. It is truly democratic in the sense that the people create the legal rights, non-violently and horizontally. Your right to make a contract with one man is your right to make a contract with everyone else, and your right to not make a contract with one man is your right to not make a contract with everyone and else. And so, if Klaus will is to create a factory, and no-one in the society he lives in is willing to create contracts for him to protect his factory, he will not, unless he is insane, invest in building a factory.
In a libertarian minarchy, protection of all property, regardless of what it will do to the rest of society, is guaranteed by the monopolistic state. If you homesteaded it, all in society are forced to recognize it. You have no choice but to acknowledge it, pay for it's protection, interact with it and be exposed to violence if you don't. All of this while it's doing things that may be directly weakening your economic situation, polluting your environment, mistreating workers, and it's all funded by your tax money. This is what I oppose when I say I oppose private property. I don't mean to limit anyone's freedom to act or create by using violence, but I don't want to have a system where a society is disempowered by a legal institution they are forced to fund and don't have any legal way of counteracting.
In a situation where law is democratized, where your consent to a legal act that affects you is the only thing that makes the legal act valid, this doesn't have to happen. You and your society is in complete control of what legal rights shall be provided, all without using violence and aggression to limit a persons own freedom to act. The society together, voluntarily, without force, sets up a set of principles they all agree on, and decides who gets power through who they give it too, by contract. It's democracy, in it's purest form.