There is no objective ownership. This isn't a controversial statement, nor is it one that people particularly lament. Sure, at times, people will decry that others don't see the value that they do in something particular, but in general I don't think that there's any serious defence of ownership being objective.
Yet, if we reflect on it for even a second, valuation of ownership is integral to our lives. We could not function even in small groups, let alone as a society, without having a set of similar values towards the notion of ownership. Among our friends and family, we may have different ways of treating ownership than we would with a stranger, but we do none the less think that our ownership is beyond the mere subjective and ought to be respected and even protected among the society we live in.
We even go so far as to teach children from a young age about the rights and obligations of ownership, and hold those who don't respect it accountable. We will gladly punish those who violate this notion, even though this valuation is by our own reckoning subjective. We have no problems recognising ownership as something that performs an integral role in our lives even though it has no meaning outside of our personal agency.
So the question is, why is it problematic if we substituted morality into the same argument? Why can't morality be useful without it needing to be true?