Just to complement my prior comment, Kevin Carson made a good point how these different theories of property could coexist in an anarchist society:
" Imagine an anarcho-capitalist community (Rothbardville) based on non-Proviso Lockean rules. An individual appeals to the community’s protection agency to enforce her property claim in a neighboring community which holds to the Ingalls-Tucker occupancy-and-use property rules, and collect rent from an occupant who refuses to recognize her title to the property. Given the enormous cost of enforcing such a claim in a community which regards it as repugnant, the anarcho-capitalist protection agency would likely have an exclusionary clause for such claims, or require the payment of an additional premium that would exceed the rental value of the property. In the mutualist community of Proudhonia, the mutual defense association would likely have a similar exclusionary clause for owner-occupants seeking protection from self-styled landlords in the anarcho-cap community. "
https://bleedingheartlibertarians.com/2012/04/in-defense-such-as-it-is-of-usufructory-land-ownership/