"In saying this, we must note that atheists are not immune from unreasoned dogma. Religion is not the only place where one can go to find doctrines that promote death and human suffering.Europe, though being more 'atheist' than America, also suffers from the influence of atheist dogmas that are as anti-science as any religion. The list of popular philosophies in Europe include post-modernism and cultural relativism, both of which condemn the idea that we can have actual knowledge of the real world. These dogmas have been as effective at holding the European culture back scientifically and economically as creationism has been in America. Focusing on religious dogmas and their harmful effects is just a part of the problem.In fact, the philosophies of post-modernism and cultural relativism point to an important case of atheist scapegoating. Many 'new atheists' have accused religious moderates of shielding religious extremists by preventing criticism against the harshest forms of their religion. However, they did not mention the fact that these non-religious philosophies are an even greater obstacle to criticizing fundamentalist religions. It's from these philosophies, not from religious moderates, that we get the idea that no culture may criticize another. Religious moderates, in contrast, still held to the possibility of moral and objective truths."
Atheistethicist.blogspot.com, Mar 6, 2008
"The general retort to relativism is simple, because most relativists contradict their thesis in the very act of stating it. Take the case of relativism with respect to morality: moral relativists generally believe that all cultural practices should be respected on their own terms, that the practitioners of the various barbarisms that persist around the globe cannot be judged by the standards of the West, nor can the people of the past be judged by the standards of the present. And yet, implicit in this approach to morality lurks a claim that is not relative but absolute. Most moral relativists believe that tolerance of cultural diversity is better, in some important sense, than outright bigotry. This may be perfectly reasonable, of course, but it amounts to an overarching claim about how all human beings should live. Moral relativism, when used as a rationale for tolerance of diversity, is self-contradictory.""It is the source of squirming internal conflict in the minds of nice liberal people who, on the one hand, cannot bear suffering and cruelty, but on the other hand have been trained by postmodernists and relativists to respect other cultures no less than their own. Female circumcision is undoubtedly hideously painful, it sabotages sexual pleasure in women (indeed, this is probably its underlying purpose), and one half of the decent liberal mind wants to abolish the practice. The other half, however, 'respects' ethnic cultures and feels that we should not interfere if 'they' want to mutilate 'their' girls."
Richard Dawkins, The God Delusion (Pages 328-9, Childhood Abuse and Religion)
"The more one learns of the different passionately held convictions of peoples around the world, the more tempting it becomes to decide that there really couldn't be a standpoint from which truly universal moral judgments could be constructed and defended. So it is not surprising that cultural anthropologists tend to take one variety of moral relativism or another as one of their enabling assumptions. Moral relativism is also rampant in other groves of academia, but not all. It is decidedly a minority position among ethicists and other philosophers, for example, and it is by no means a necessary presupposition of scientific open-mindedness.
We don't have to assume that there are no moral truths in order to study other cultures fairly and objectively; we just have to set aside, for the time being, the assumption that we already know what they are."
Daniel C. Dennett, Breaking The Spell (Pages 375-6, Some More Questions About Science)
Anyway, with relativism this whole New Atheist thing would be meaningless, and no-one would care.
Consider these facts:1. The Pope in particular, and a lot of other religious conservatives constantly raise the point about relativism, as a disease of modern society. The underlying (or overt) message is that without God, there's not point in being moral, and that secularism will lead to relativism. Their major gripe with modernity is that morality has become a matter of opinion.(I subscribe to a Google News feed that gives me a note in the Google Reader whenever there's a news item with the word "relativism" mentioned. The Pope crops up regularly, and most of the others tend to be religious conservatives attacking secularism.)2. Most of the non-religious criticism levelled at the New Atheists come from relativists. We're angry, militant, while there are "other truths", there should be tolerance, dialogue and so on and so on. They may not identify as relativists, or use that word at all, but they usually have that kind of understanding.

It's a triple problem and that's why it must be combated. When the Pope attacks secularism for leading us into relativism, we can't simply deny this. Those of us who aren't relativists will shout straw man!, and while that is true - for most of us - there is still some people who are attracted by it. We can't simply dismiss relativism as a non-problem.
There is one more thing I want to add. Conservative and fundamentalist believers are of course making a false dichotomy where you have to chose between their absolutism or relativism. And also defenders of relativism have been using the same logic.
"Since such relativism is intolerable, in their eyes, imperialist universalism must be endorsed. Either we're right and they're wrong, or "right" and "wrong" have no meaning!" DennettSo make no mistake, there are things in other cultures that are perfectly fine. It's just that the proponents of relativism seem not to separate between FGM and spicy food.

"God's mysterious ways" = "God's culture" in relativist language.