Subjectivism requires that moral claims have truth values which , in principle, dpened on the individual making them

This is not true of all subjectivisms, as the link makes totally clear. Subjective simply means that something is mind-dependent; it need not be the mind of the person making the claim-- or not only the mind of the person making the claim. For instance, the facts that determine whether or not a moral claim is true could consist in just the moral opinions and attitudes where all humans overlap.