Is Morality Objective?

[Thumpalumpacus]

what one person considers the referent can differ from another's. 

That makes it vague, not subjective. As long as it is agreed upon that the referent exists objectively, the concept is also objective, no matter how vague it is.

But that doesn't apply to morality. What is moral for one person can be immoral for another person, because morality is an abstraction.

Humans are fond of using moral referents as absolutes, but that doesn't mean that they are indeed absolute. Human morality is based upon perspective. Consider killing another human: in some cases we regard that as murder, in other cases we regard that as more acceptable morally (due to self-defense reasons, defense of others, and so on).

The moral value of killing another human is contingent on the circumstances surrounding the killing. That makes the morality of such a killing relative.

And because the circumstances of a killing are colored by the perspective of the killer and the victim, the morality of such an act is not only relative, but subjective.

There's no moral precept that exists independently of the human mind. One cannot point to anything not arising from humans (with their perspectives and foibles) and say "this is why my act was moral." One can only appeal to human judgement regarding this or that action. This is why all moral judgements are both relative and subjective.