In "What Really Scares the New Atheists", John Gray argues that Friedrich Nietzsche represents the type of morality that New Atheists haven't really dealt with. Unlike the New Atheists today, who absurdly argue that science can support a liberal morality, as a classical scholar, Nietzsche recognized the imprints of Christianity on liberal morality and, from that recognition, created a scathing critique of both Christianity and liberalism. Mr Gray writes:
The new atheists rarely mention Friedrich Nietzsche, and when they do it is usually to dismiss him. This can’t be because Nietzsche’s ideas are said to have inspired the Nazi cult of racial inequality – an unlikely tale, given that the Nazis claimed their racism was based in science. The reason Nietzsche has been excluded from the mainstream of contemporary atheist thinking is that he exposed the problem atheism has with morality. It’s not that atheists can’t be moral – the subject of so many mawkish debates. The question is which morality an atheist should serve.
It’s a familiar question in continental Europe, where a number of thinkers have explored the prospects of a “difficult atheism” that doesn’t take liberal values for granted. It can’t be said that anything much has come from this effort. Georges Bataille’s postmodern project of “atheology” didn’t produce the godless religion he originally intended, or any coherent type of moral thinking. But at least Bataille, and other thinkers like him, understood that when monotheism has been left behind morality can’t go on as before. Among other things, the universal claims of liberal morality become highly questionable.
It’s impossible to read much contemporary polemic against religion without the impression that for the “new atheists” the world would be a better place if Jewish and Christian monotheism had never existed. If only the world wasn’t plagued by these troublesome God-botherers, they are always lamenting, liberal values would be so much more secure. Awkwardly for these atheists, Nietzsche understood that modern liberalism was a secular incarnation of these religious traditions. As a classical scholar, he recognised that a mystical Greek faith in reason had shaped the cultural matrix from which modern liberalism emerged. Some ancient Stoics defended the ideal of a cosmopolitan society; but this was based in the belief that humans share in the Logos, an immortal principle of rationality that was later absorbed into the conception of God with which we are familiar. Nietzsche was clear that the chief sources of liberalism were in Jewish and Christian theism: that is why he was so bitterly hostile to these religions. He was an atheist in large part because he rejected liberal values.
Bill Vallicella has a worthwhile commentary on this specific point, "Nietzsche and the New Atheists", at Maverick Philosopher. The challenge that Nietizsche presents to atheists, New and otherwise, is that they have to be careful about how they talk about morality. In the West, people take a Christian framework for granted and don't realize that terms like 'rights' or 'equality' are nonsense sans God. The challenge isn't an argument for God's existence; rather, a call for atheists to take the nihilism that their worldview implies seriously.