This piece by Boston Globe columnist Jeff Jacoby (whose work I generally like) is an excellent illustration of what is probably the most common fallacy in discussions about atheism - the belief that atheism necessarily leads to moral relativism:
What society loses when it discards Judeo-Christian faith and belief in G-d is something far more difficult to replace: the value system most likely to promote ethical behavior and sustain a decent society. That is because without G-d, the difference between good and evil becomes purely subjective. What makes murder inherently wrong is not that it feels wrong,but that a transcendent Creator to whom we are answerable commands: "Thou shalt not murder...."
Obviously this doesn't mean that religious people are always good, or that religion itself cannot lead to cruelty. Nor does it mean that atheists cannot be beautiful, ethical human beings. Belief in G-d alone does not guarantee goodness. But belief tethered to clear ethical values — Judeo-Christian monotheism — is society's best bet for restraining our worst moral impulses and encouraging our best ones.
The atheist alternative is a world in which right and wrong are ultimately matters of opinion, and in which we are finally accountable to no one but ourselves.
Jacoby's claim that atheism is antithetical to morality is far from unusual. As I note here, survey data shows that 51% of Americans believe that "“[i]t is necessary to believe in God in order to be moral and have good values” (thereby going even farther than Jacoby, who concedes that atheists can be "ethical human beings").
While some atheists are moral relativists, there is no necessary connection between the two beliefs. Atheists, like theists, can have strong commitments to objective views of morality based on reason, tradition, communitarianism, and so on. There is absolutely no reason why atheists can't have "clear ethical values" just as much as theists do. Indeed, most prominent atheist thinkers (consider, for example, Karl Marx or Ayn Rand) argue for very strong non-relativist views of morality. The standard form of the argument that atheism=moral relativism implicitly assumes that belief in a deity is the only possible source of moral values; but that assumption is simply wrong.
In the last paragraph of his column, Jacoby hints at a more moderate defense of the atheism=relativism equation. Perhaps atheists can have nonrelativist views of morality, but the lack of a single divine authority for moral principles leads to disagreement and a reduction in the certainty with which people hold their moral beliefs - thereby causing a widespead perception that "right and wrong are just matters of opinion." Maybe so (though I am skeptical), but theists have exactly the same problem. After all, they disagree amongst themselves about 1) what kind of God or gods exist, and 2) what the relevant deity or deities want us to do. Disagreement over moral issues between different groups of theists is every bit as deep as that between divergent secular views of morality. If the latter could persuade people that right and wrong are matters of opinion, so too could the former. Even if we limit our focus to the "Judeo-Christian" tradition to which Jacoby refers, there is still tremendous disagreement between different groups within the Christian tradition (to say nothing of the deep disagreement between Christians and Jews that the term "Judeo-Christian" is often used to elide).
Finally, it is possible to argue that, even absent any logical connection between atheism and relativism, atheists in fact are empirically more likely to be moral relativists than theists. I have not seen evidence definitely settling this issue either way. But even if the empirical claim is true, it doesn't follow that atheism is dangerous.
This is so for three reasons. First, it could be that the causation runs from moral relativism to atheism rather than the other way around. People attracted to moral relativism may become atheists as a result rather than vice versa. Second, even if the causation runs in the direction that critics of atheism posit, the harm caused by an increasing prevalence of moral relativism must be weighed against the harm caused by non-relativist, but deeply flawed views of morality. I would rather live in a society dominated by selfish moral relativists than one dominated by nonrelativist believers in Nazism, Communism, or radical Islamism. Whether increasing moral relativism is harmful depends on what values people give up to become relativist.
Finally, even if increasing moral relativism is indeed socially dangerous, there may be ways of persuading atheist moral relativists to give up moral relativism without also giving up atheism. Just as religious groups often successfully persuade theists to convert from one religion to another, it may be that some moral relativist atheists can be persuaded to become moral objectivists. Indeed, to the extent that becoming an atheist does cause people to become moral relativists, it may be because of the widespread prevalence of views of like Jacoby's. Some who conclude that God does not exist may also come to believe that there is no objective morality because they (like Jacoby) wrongly assume that the latter is a necessary implication of the former.
Thus, those who worry about the alleged trend towards moral relativism might be better advised to oppose it by emphasizing that moral objectivism is compatible with a wide range of views on religion, including atheism.