I know "relativism" is often a dirty word among many skeptics, but I find that this is generally based on a conflation of any kind of "relativism" with "moral relativism." Cultural relativism as introduced by Boas is simply a method of anthropological inquiry that says that the best way to understand why a culture is the way it is (or why people within a society do things in a certain way) is to gain an emic (or insider's) understanding. Cultural relativism as a method is the rejection of ethnocentrism when trying to learn about other societies. Cultural relativism should not be conflated with moral relativism, which is the idea that there are no objective or absolute moral or ethical standards such that morals should never be judged as objectively good or bad. Cultural relativism is a method that seeks to suspend value judgments in order to understand a particular phenomenon. Anthropologists also draw on an eitc (outsider's) understanding, not during the process of data collection but during data analysis and writing the ethnography.The skeptics and atheist communities do have a "thing" about cultural relativism. I'd add add two more reasons to Will's observation.
Moral relativism has very little to do with Boasian cultural relativism. Boas himself held very strong views about the morality of racism and human rights. For Boas (and for American anthropologists today), an attempt to approach other cultural systems with dispassionate objectivity (i.e., cultural relativism) did not entail moral disengagement from the world (i.e., moral relativism). In this way, Boasian cultural relativism is an attempt to apply scientific objectivity to the study of human culture.
1) These are movements established around being right about the wrongness of certain beliefs--pseudo-science, alternative medicine, god. Confronting these beliefs is important. That's not a point I need to stress. But it isn't something I consider "fun", at least after a certain point. There is pleasure in demolishing someone with a well rehearsed set of arguments, but I have to admit it is a bit of a douchey pleasure. But there are other engagements with difference, where it is not clear who is right and wrong. These engagements are rewarding, but in another way.
Anthropology is about this second type of engagement, about understanding people who have different beliefs, rather than proving them wrong. On a practical level, as a basis for action, understanding why people have obviously wrong beliefs is more useful than simply proving those beliefs wrong over and over. Right there, that makes anthropology an object of suspicion for many skeptics. For these skeptics, difference entails someone being right and someone being wrong. I wonder if this attitude might be part of the current skeptical/atheist meltdown over the treatment of people who are different (i.e., not white cisgendered males).
2) Another problem is the charismatic figures of the skeptic/atheist movement, such as Christopher Hitchens and Richard Dawkins, are not exactly examplars of cultural understanding. Part of their appeal is the decisiveness and clarity that comes with moral certainty.
Finally, as Will says, cultural relativism tends to be a huge straw man, being conflated with an undefined series of "fings wot I don't like"--things like postmodernism, political correctness, and multiculturalism. This seems to be true even with relatively thoughtful skeptics.
Most skeptics' understanding of cultural relativism probably comes from these two paragraphs in Dawkin's 1995 book River out of Eden.
There is a fashionable salon philosophy called cultural relativism which holds, in its extreme form, that science has no more claim to truth than tribal myth: science is just the mythology favored by our modern Western tribe. I once was provoked by an anthropologist colleague into putting the point starkly, as follows: Suppose there is a tribe, I said, who believe that the moon is an old calabash tossed into the sky, hanging only just out of reach above the treetops. Do you really claim that our scientific truth-that the moon is about a quarter of a million miles away and a quarter the diameter of the Earth-is no more true than the tribe's calabash? "Yes," the anthropologist said. "We are just brought up in a culture that sees the world in a scientific way. They are brought up to see the world in another way. Neither way is more true than the other."
Show me a cultural relativist at thirty thousand feet and I'll show you a hypocrite. Airplanes built according to scientific principles work. They stay aloft, and they get you to a chosen destination. Airplanes built to tribal or mythological specifications, such as the dummy planes of the cargo cults in jungle clearings or the beeswaxed wings of Icarus, don't.* If you are flying to an international congress of anthropologists or literary critics, the reason you will probably get there-the reason you don't plummet into a ploughed field-is that a lot of Western scientifically trained engineers have got their suns right. Western science, acting on good evidence that the moon orbits the Earth a quarter of a million miles away, using Western-designed computers and rockets, has succeeded in placing people on its surface. Tribal science, believing that the moon is just above the treetops, will never touch it outside of dreams.[Damn, if nothing else Dawkins is a formidable quotable sound-bite producing machine. Let me tell you, having the basic underpinning of anthropology and archaeology (both fieldwork-oriented disciplines) dismissed as "fashionable salon philosophy," and by Richard Dawkins of all people, is a bracing experience.]
I realise Dawkin's isn't really making a scholarly argument here, merely pandering to his base, but it still an awesomely ignorant argument. He is making the standard mistake of conflating cultural relativism with epistemological relativism and what is no doubt postmodernism. He does try to put a fig leaf over his nonsense by the use of "in its extreme form" and a rather dubious anecdote, but it is nonetheless an outrageous straw man.
At its core cultural relativism is, as Will notes, an attempt to apply scientific objectivity to the study of human culture. There is some element of at least the popular understanding of moral relativism involved, in that a suspension of moral judgment is required (the content of morality being cultural). Think about it. In what field does one approach one's object with prejudice (i.e pre-judgement) as a valid tool? Does a biologist judge some animals as "good" and some as "bad" based on ideology? Would you take your car to a mechanic who reached decisions based on whether he thought the engine was good or evil? Probably not.
Anthropology is the study of human variation--cultural, linguistic and physical--across and through time. Humans are the anthropological object of study. Cultural relativism is the appropriate scientific stance for the study of human variation. If you disagree with this, then what is the appropriate stance? As a basis for action in the world, explanations like "their beliefs suck" and "they are evil and hate our freedoms" have not worked out so well. If a group has beliefs we find reprehensible, it is still worthwhile, and practically more useful, to find out why they have those beliefs.
I will be honest, the fact of the object of anthropology is people complicates things no end. It would not surprise me if Dawkin's anecdote is true. Anthropologists' "objects" are subjects, who study us back, and we are implicated with them through multiple sets of relations, relations that do not play a role in the considerations of, say, physicists or biologists. Anthropologists have responsibilities and obligations that other fields do not. There is debate within the field as to what cultural relativism means beyond being an objective perspective. But if you are going to take issue with cultural relativism as something other than a neutral stance for the study of human difference, you then need to be explicit about who you are talking about and what their arguments are. Cutesy anecdotes about anonymous anthropologists are not useful.
1995 A River out of Eden: A Darwinian View of Life. BasicBooks, New York, NY.