Scholars disagree about whether he should be classified as a relativist, but his thought certainly has a pronounced relativistic thrust.
After all, every society might agree that homosexuality is wicked or that men should have dominion over women. The many different interpretations of quantum mechanics are a case in point. The argument obviously rests on the idea that moral objectivism has been discredited.
Here is for instance Harvey Siegel: This incoherence charge is by far the most difficult problem facing the relativist. This charge seems to have some purchase on the sort of relativism that treats the validity of moral claims as relative to specific identifiable cultures.
Ancient Greece In the view of most people throughout history, moral questions have objectively correct answers. Even though moral relativism makes its first appearance in ancient times, it hardly flourished.
Ethical Non-Realism Ethical non-realism is the view that there is no objective moral order that makes our moral beliefs true or false and our actions right or wrong. Presents a version of moral relativism based on an analysis of what it means for someone to have a reason to do something.
Boas viewed cultural relativism—a commitment to understanding a society in its own terms—as methodologically essential to scientific anthropology.
On the Genealogy of Morals.