Aside from the fact that there is no workable argument for Moral relativism as a viable moral theory, and that Moral Relativism would lead to absurd corollaries with which no one could agree, there is a huge problem with Moral Relativism in the public square:
If, as my friend Rodak insists, the state must maintain an orthodoxy of moral relativism, upon what is the state to base its laws? Law must be based on morality. If it is not, then what is it based on? The tyranny of the majority? Bigotry? Prejudice? Self interest of the powerful? The dictates of the powerful?
No doubt you ask, “But which theory?” That is a good question, and would make for an interesting discussion, but we have to take things one at a time. Before going into that, first we should consider the matter in the abstract.
What do we base out law on if not objective morality.