It's not really the effort to protect, but whether you see it as a choice society can legitimately make, or something inherent pre-existing society. Is private property something that a society should recognize or not recognize based on pragmatic reasons, like how well society functions as a result? Or is private property some sort of inherent/moral right (as e.g. John Locke and most libertarians argue)? A similar debate comes up with copyright: is it a privilege that we as a society choose to recognize as a means of encouraging the production of creative works? Or is it some sort of inherent/moral right of a creator to control the reuse of their works?

In a given context, rights can be more or less fundamental. Imagine a hypothetical post-scarcity society. Protection of private property in our sense ceases to have meaning there and cannot be considered a right. How can anyone of sound mind mistake private property as a natural right in light of such thought experiments? It's a contingent and therefore non-absolute right.

You can consider protection of private property the most important right in societies like ours, so important it occupies a lofty stratum of its own, and yet not commit the fallacy of claiming that private property is a natural right. However, it's understandable why people with priorities like that would make such a mistake.

It seems to me that, somewhat like adultery, most people treat infringement against their property as threat to some stone age survival instinct. We can hear it when a small child shouts "MINE!" and see it in the cumbersome hoards of garbage some homeless people drag around. I doubt a post-scarcity society will be able to coolly regard all stuff as ephemeral and fungible; we'll still defend our stuff vigorously only there will be more of it.

This is why "infringement is theft" arguments are so manipulative and dishonest. They try to tap into this indignation rather than win the debate on the merits.

What makes some rights more inherent than others? Some people seem to think that a right can be inherent in an absolute almost mathematical sense. This is a lack of imagination. Many rights that seem inherent now were not in the past and are not going to be in the future.

Rights should be judged by their usefulness, not by how fundamental some person thinks they are, because no right is truly fundamental.

You're right in that nature gives us no rights. Maybe it would be better to say God-given rights. Thus the command "Thou shalt not steal" becomes the basis of property rights. These rights can be understood as universal as I know of no culture in which it is considered a virtue to steal.