There are also plenty that would insist that insisting on a right to property is fundamentally incompatible with liberty, and can even be incompatible with a right to life (e.g. if enforcement of property rights de facto takes away peoples realistic ability to provide for themselves).
EDIT: We even have good historical examples of the latter, such as the Great Famine in Ireland, where food exports continued - people died because other peoples property rights were put before their right to life, and people had no realistic prospect of acquiring or growing food in time to compensate for the crop failures. Notably, in contrast, in at least one past famine, the government had banned food exports to force prices down.
"if enforcement of property rights de facto takes away peoples realistic ability to provide for themselves"
Removal of property rights intrinsically takes people's ability to provide for themselves away and replaces it with dependency. Some people seem to prefer this arrangement and I can respect that, but when they describe it as 'liberty', I assume that they must have lost their minds.
You are jumping to the conclusion that any removal of property rights intrinsically and automatically removes peoples ability to make use of property.
That is a direct parallel to the entire point of the "property is theft" argument: that strict enforcement of property rights is a limitation on peoples ability to make use of property, by monopolising use of it.
You can destroy the ability to make use of property by going too far either way.
A good example of how carveouts can increase the ability of people to make use of property and improve their ability to provide for themselves is the Scandinavian "freedom to roam": In Norway anyone can use "outland" - areas that are not part of urban settlement. Owning the land gives you a monopoly on certain users (e.g. you will own hunting rights and forestry rights, for example) but far fewer than most other places.
Apart from providing liberty in the form of being able to go where we want without having to ask permission of land owners, for centuries this has been an important means for people to help provide for themselves: Nobody can deny you the ability to e.g. pick berries or mushrooms, or let your sheep graze, for example. It provides a substantial increase in utility of land that would often see substantially less use, and makes a lot of people able to be independent and work for themselves instead of someone else. That is one way it can increase liberty.
In a functioning society, there are always going to be rules. Rules depend on someone or something enforcing them. If a society decides to adopt 'liberty' defined as the lack of all rules and no enforcement to create the dependency you mention, then this will merely breed a different kind of rules. Whoever is strongest will make the new rules and liberty will disappear as quickly as is was put in place.
Defining liberty as an absence of dependency cannot work in any society because it's going to degenerate into an unfree one more or less immediately. What's worthwhile to pursue is that all rules apply to everyone in the same way and that everyone has a realistic opportunity to shape the rules together with all the other people. This means participation in the political process, division of powers, transparency to avoid corruption, education for everyone, and enough executive power to prevent some random billionaire from unilaterally seizing power. It does not mean abolishing the organization tasked with guaranteeing those rights.
If you choose to give up your life in the pursuit of liberty, that's great for you and great for us.
But rights are things that circumscribe government actions, not individuals. A government's first job and most important job is to safeguard the lives of it's citizens. Liberty is it's second job.
I suspect the real reason for this is that security is easier to define and agree on than liberty is. Ditto for property vs liberty.
John Locke wrote of "life, liberty and property".