Cultural moral relativism is the view that what is morally right and wrong varies between cultures. According to normative cultural moral relativism, what varies between cultures is what really is morally right and wrong (e.g., in some cultures, slavery is genuinely permissible, in other cultures it isn't). According to descriptive cultural moral relativism, what varies is what people in different cultures think is right and wrong (e.g., in some cultures people think slavery is fine, in others they don't; but the position is neutral on whether slavery really is fine in the cultures that think it is). A strong version of descriptive cultural moral relativism holds that cultures vary radically in what they regard as morally right and wrong.
However, I reject this view. My experience with ancient Chinese philosophy is the central reason.
Here are the first passages of the Analects of Confucius (Slingerland trans., 2003):
1.1. The Master said, "To learn and then have occasion to practice what you have learned -- is this not satisfying? To have friends arrive from afar -- is this not a joy? To be patient even when others do not understand -- is this not the mark of the gentleman?" 1.2. Master You said, "A young person who is filial and respectful of his elders rarely becomes the kind of person who is inclined to defy his superiors, and there has never been a case of one who is disinclined to defy his superiors stirring up rebellion. The gentleman applies himself to the roots. 'Once the roots are firmly established, the Way will grow.' Might we not say that filial piety and respect for elders constitute the root of Goodness?" 1.3. The Master said, "A clever tongue and fine appearance are rarely signs of Goodness." 1.4. Master Zeng said, "Every day I examine myself on three counts: in my dealings with others, have I in any way failed to be dutiful? In my interactions with friends and associates, have I in any way failed to be trustworthy? Finally, have I in any way failed to repeatedly put into practice what I teach?"No substantial written philosophical tradition is culturally farther from the 21st century United States than is ancient China. And yet, while we might not personally endorse these particular doctrines, they are not alien. It is not difficult to enter into the moral perspective of the Analects, finding it familiar, comprehensible, different in detail and emphasis, but at the same time homey. Some people react to the text as kind of "fortune cookie": full of boring and trite -- that is, familiar! -- moral advice. (I think this underestimates the text, but the commonness of the reaction is what interests me.) Confucius does not advocate the slaughter of babies for fun, nor being honest only when the wind is from the east, nor severing limbs based on the roll of dice. 21st century U.S. undergraduates might not understand the text's depths but they are not baffled by it as they would be by a moral system that was just a random assortment of recommendations and prohibitions.
You might think, "of course there would be some similarities!" The ancient Confucians were human beings, after all, with certain natural reactions and who needed to live in a not-totally-chaotic social system. Right! But then, of course, this is already to step away from the most radical form of descriptive cultural moral relativism.
Still, you might say, the Analects is pretty morally different -- the Confucian emphasis on being "filial", for example -- that's not really a big piece of U.S. culture. It's an important way in which the moral stance of the ancient Chinese differs from ours.
This response, I think, underestimates two things.
First, it underestimates the extent to which people in the U.S. do regard it as a moral ideal to care for and respect their parents. The word "filial" is not a prominent part of our vocabulary, but this doesn't imply that attachment to and concern for our parents is minor.
Second, and more importantly, it underestimates the diversity of opinion in ancient China. The Analects is generally regarded as the first full-length philosophical text. The second full-length text is the Mozi. Mozi argues vehemently against the Confucian ideal of treating one's parents with special concern. Mozi argues that we should have equal concern for all people, and no more concern for one's parents than for anyone else's parents. Loyalty to one's state and prince he also rejects, as objectionably "partial". One's moral emphasis should be on ensuring that everyone has their basic necessities met -- food, shelter, clothing, and the like. Whereas Confucius is a traditionalist who sees the social hierarchy as central to moral life, Mozi is a radical, cosmopolitan, populist consequentialist!
And of course, Daoism is another famous moral outlook that traces back to ancient China -- one that downplays social obligation to others and celebrates harmonious responsiveness to nature -- quite different again from Confucianism and Mohism.
Comparing ancient China and the 21st century U.S., I see greater differences in moral outlook within each culture than I see between the cultures. With some differences in emphasis and in culturally specific manifestations, a similar range of outlooks flourishes in both places. (This would probably be even more evident if we had more than seven full-length philosophical texts from ancient China.)
So what about slavery, aggressive warfare, women's rights, and the rest? Here's my wager: If you look closely at cultures that seem to differ from ours in those respects, you will see a variety of opinions on those issues, not a monolithic foreignness. Some slaves (and non-slaves) presumably abhor slavery; some women (and non-women) presumably reject traditional gender roles; every culture will have pacifists who despise military conquest; etc. And within the U.S., probably with the exception of slavery traditionally defined, there still is a pretty wide range of opinion about such matters, especially outside mainstream academic circles.