Descriptive Moral Relativism (DMR). As a matter of empirical fact, there are deep and widespread moral disagreements across different societies, and these disagreements are much more significant than whatever agreements there may be.
(Metaethical moral relativism is the view that the real -- and not just perceived -- truth or falsity of moral claims varies from society to society. Since philosophers generally don't accept metaethical moral relativism unless they accept descriptive moral relativism, I focus on the descriptive thesis.)
Some of my favorite empirically-oriented philosophers of psychology -- Jesse Prinz, John Doris, Stephen Stich, and Shaun Nichols -- have recently avowed moral relativism. But I can't agree.
My argument against relativism is simple. There is no culture with a written philosophical tradition that is farther removed from the contemporary West than is ancient China. Yet the moral thought expressed by philosophers of the period is remarkably similar to our own. Consider, to take an arbitrary sample, the first five passages of Confucius's (Kongzi's) Analects, the most important philosophical text of the period (D.C. Lau, trans.):
I.1. The Master said, "Is it not a pleasure, having learned something, to try it out at due intervals? Is it not a joy to have friends come from afar? Is it not gentlemanly not to take offense when others fail to appreciate your abilities?"
I.2. Yu Tzu said, "It is rare for a man whose character is such that he is good as a son and obedient as a young man to have the inclination to transgress against his superiors; it is unheard of for one who has no such inclination to be inclined to start a rebellion. The gentleman devotes his efforts to the roots, for once the roots are established, the Way will grow therefrom. Being good as a son and obedient as a young man is, perhaps, the root of a man's character."
I.3. The Master said, "It is rare, indeed, for a man with cunning words and an ingratiating face to be benevolent."
I.4. Tseng Tzu said, "Every day I examine myself on three counts. In what I have undertaken on another's behalf, have I failed to do my best? In my dealings with my friends have I failed to be trustworthy in what I say? Have I passed on to others anything that I have not tried out myself?"
I.5. The Master said, "In guiding a state of a thousand chariots, approach your duties with reverence and be trustworthy in what you say; avoid excess in expenditure and love your fellow men; employ the labor of the common people only in the right seasons."
In these passages, Confucius and his school praise honesty, moderation, concern for others, obedience to authority, and humility. They don't say: Kill your relatives for fun, never pay your debts, burn down your neighbors' houses. Nor does any other major school of philosophical or religious thought, no matter how far culturally removed. Indeed, it's hard to see how a society could survive with such a morality.
Though the points of commonality far exceed the points of difference, the ancient Confucian tradition does differ from mainstream U.S. ethics in some important secondary ways -- most notably in demanding a high level of respect for parents and elders and in their emphasis on following ritual and custom. However, other philosophers within the ancient Chinese tradition criticize the Confucians for these very things, such as Mozi and Zhuangzi. So also in the U.S. we have libertarians and fundamentalists, Earth First!ers and yuppies. The real diversity of moral opinion is more to be found within ancient China and within the contemporary U.S. than between the two cultures. (But even that diversity isn't so great, if one keeps a broad view and excludes the deranged and those who merely thrill at being provocative.)