Myth:
When atheists reject the religion in which they have been raised, they tend to keep the morality while discarding its theological foundation. Their ethical behavior is thus derivative and parasitic, borrowing its conscience from a culture permeated by religion; it cannot survive if the surrounding religious culture is not sustained. In short, morality as we know it cannot be maintained without Judeo-Christian religion.
Response:
A popular argument used by Christians against atheists is to claim that atheists are only moral because they have inherited moral values from the "Christian" cultures in which they live. According to these Christians, secularists and atheists are living off the accumulated "moral capital" created by Christianity over centuries. If Christianity ceases to be a binding social, political force, that capital will no longer be created and will instead just be depleted until the well runs dry.
Basically, this argument is saying that while atheists may be moral, may believe in fairness, and may feel empathy, it's only a temporary state of affairs. The morality, fairness, and empathy of atheists is "explained" by claiming that they aren't immoral yet, but they will be soon enough. No mater how moral or fair atheists behave, Christians can always come back to claim that it's only because the moral capital of Christianity hasn't been entirely depleted yet.
Perhaps the most important thing to note about this argument is that it is unfalsifiable. If atheists behave immorally, it's because they have used up all their accumulated moral capital and now we're seeing the real consequences of atheism. If atheists behave morally, it's only because they haven't used up their accumulated moral capital and aren't immoral yet. Not a single shred of evidence in support of this argument is ever offered, and not a single shred of evidence could ever disprove it. In short, it's nothing more or less than a faith position designed to perpetuate anti-atheist bigotry.
Another problem with the claim is that there are really two claims: first that atheists have only learned their morality from the Christian context in which they live, and second that atheists' morality can only be sustained by the continuation of a Christian context to live in. The first claim is more believable than the second: culture carries on many practices and value which were originally developed in one context and then ultimately survived its original justifications. To cite a trivial example, women's shirts button the opposite from men's for reasons that are no longer applicable.
It's thus not unreasonable to suggest that at least some of the moral reasoning used by atheists is dependent upon earlier Christians beliefs which atheists no longer accept. This is not really a criticism, though, because the same can be said about anyone Christians certainly employ Greek standards and reasoning which have been incorporated into Christian theology and preserved long after the original context was abandoned. If Christians can do it with Greek ideas, why can't atheists do it with Christian and Greek ideas?
The second claim, that atheists' morality cannot survive without reinforcement from Christian culture, is not the least bit reasonable. This claim depends upon the assumption that any ideas or arguments atheists might have inherited from Christianity cannot survive outside a Christian context, but absolutely no evidence is provided for this. Christians don't even provide evidence for something like this happening in other contexts, much less with Christianity itself.
Sometimes Christians making this argument attempt to support it by pointing to moral and political changes in societies that have become less Christian and more secular for example, the legalization of abortion, the tolerance of homosexuality, and increases in unwed pregnancies. This sort of "evidence" presumes the truth of disputed Christian moral claims, however, and thus commits the fallacy of Begging the Question. Christians adopting this line of argument also ignore the ways in which these societies have changed for the better: greater equality, greater democracy, etc.
There are many other serious flaws in this myth as well. For one thing, it assumes that whatever morality a person had while they were Christian, it was necessarily and entirely Christian in nature. There is no evidence for this either, but there is considerable evidence that Christians derive their moral sense from culture, society, and politics as well. The above myth also assumes that whatever morals Christianity teaches cannot be justified by or derived from any other belief system, such that once a person abandons Christianity they no longer have any basis for accepting the same moral positions they believed before. This may indeed be the case with some moral propositions, but it's obviously not the case with others if it were, then only Christians would be moral.
In the end, this myth is a form of aggressive and arrogant bigotry against all non-Christians although it may sometimes be expressed in a manner that promotes religion generally, it is usually phrased to promote Christianity in particular. It's bigoted against atheists, obviously, because it is directed at them and is designed to argue that atheists are incapable of either being moral themselves or of sustaining a moral society. It's also bigoted against non-Christians because it asserts that only Christianity is capable of sustaining a moral society. It is even bigoted against Jews, despite mentioning them in a half-hearted way, because a Jewish society would utilize a Jewish morality, not a Judeo-Christian morality.

