This position - that ethical statements have no truth value, that one moral position is as good (and as false) as any other - amounts to a denial of reason, and ends up closer to nihilism than even the much-maligned David Benatar, who at least recognizes the universal value of preventing suffering.
With this sort of laziness in mind, Thomas Nagel has this to say about the denial of the reality and universality of moral reason:
To reason is to think systematically in ways anyone looking over my shoulder ought to be able to recognize as correct. It is this generality that relativists and subjectivists deny. Even when they introduce a simulacrum of it in the form of a condition of consensus among a linguistic or scientific or political community, it is the wrong kind of generality - since at its outer bounds it is statistical, not rational.
The worst of it is that subjectivism is not just an inconsequential intellectual flourish or badge of theoretical chic. It is used to deflect argument, or to belittle the pretensions of the arguments of others. Claims that something is without relativistic qualifications true or false, right or wrong, good or bad, risk being derided as expressions of a parochial perspective or form of life - not as a preliminary to showing that they are mistaken whereas something else is right, but as a way of showing that nothing is right and that instead we are all expressing our personal or cultural points of view. The actual result has been a growth in the already extreme intellectual laziness of contemporary culture and the collapse of serious argument throughout the lower reaches of the humanities and social sciences, together with a refusal to take seriously, as anything other than first-person avowals, the objective arguments of others. . . .
Many forms of relativism and subjectivism collapse into either self-contradiction or vacuity - self-contradiction because they end up claiming that nothing is the case, or vacuity because they boil down to the assertion that anything we say or believe is something we say or believe. I think that all general and most restricted forms of subjectivism that do not fail in either of these ways are pretty clearly false.