Value is an expression of subjective preference. Subjective preferences are expressed with the objective of reducing some feeling of uneasiness through purposeful action, and with the expectation that the chosen means will result in the desired end.
This universal truth is called "the action axiom".
It is the objective of ALL purposeful actors to reduce felt uneasiness through purposeful action which puts some scarce means to use for the purpose of attaining some desired end.
This means there are objective, universal values core to all purposeful actors which give rise to each individual's ability to express their subjective preferences in the first place.
Two scarce, rivalrous means involved in every purposeful act are the purposeful actor's body and time. Due to the uneasiness felt by each purposeful actor, it is not possible for the purposeful actor to remain indifferent with regard to these means. No one has a higher claim to these scarce means than the individual purposeful actor him or herself. Their body is theirs, thus they may exclude others from the use of it as they see fit so that they may employ their body toward uses they personally prefer.
Different purposeful actors have different preferences with regard to how scarce, rivalrous means should be used - including the bodies and time of other purposeful actors (hence the term "rivalrous"). No scarce means can be simultaneously employed toward ends which are exclusive to each other.
This is why morality and property rights are established: to mitigate and address conflict among purposeful actors over scarce, rivalrous means. Morality and property rights are therefore exclusively the domain of situations involving the property of more than one purposeful actor (or future purposeful actor, as is the case with small children). "Property" speaks to first use or consensual exchange of a scarce resource; "morality" speaks to the negative obligation of non-aggression which arises from first use and consensual exchange.
When someone initiates force against the scarce means of a purposeful actor to interfere with that purposeful actor's expression of subjective preference, it subsequently results in an increase in felt uneasiness for the owner of that means. This is universally true. Since property rights and morality are established with the objective of avoiding and addressing conflict over scarce resources, it is objectively immoral for any purposeful actor to trespass against the body or property of any other purposeful actor without mutual consent. Doing so temporarily or permanently excludes a purposeful actor from using their own scarce means to express their own subjective preferences, which is antithetical to liberty, morality and property. If someone consented to such a trespass, it would be because they expected to benefit from it, thus aggression wouldn't be necessary and it wouldn't be a trespass.
It's not possible to reject the non-aggression principle or the property norms from which it arises through conversation without demonstrating a preference for property norms vis a vis ownership of one's own body. Any attempt to do so constitutes a performative contradiction. That means it's impossible to put forth a case for the subjectivity of morality without contradicting oneself.