One of the many things Augustus boasted of in his Res Gestae, which he thoughtfully had inscribed for our benefit in various parts of the empire, was his assiduous restoration and dedication of temples of the gods. He names those who were so honored, but I won't repeat them here.
Augustus and others of his time were concerned that Rome had gone astray by forgetting or at least ignoring ancestral pieties. As a result, Rome had been plunged into civil war, and its citizens were degenerating, indulging in innumerable vices and sometimes succumbing to the depraved charms of outlandish religions, primarily of weird, oriental (decidedly un-Roman) origins. Augustus therefore felt it necessary to legislate morality, and actively preached the benefits of the simple, rigorous, religious and chaste lifestyle of the old Romans in the Senate and elsewhere. If Suetonius and others are any indication, he was ignored by most Romans, including members of his family in particular. Nevertheless, he was cheered on in his efforts by many, including Horace and Virgil.
Of course, this is a story we're familiar with; indeed its been repeated so often that this familiarity may be seen to breed a certain contempt. We hear today as we've heard for centuries that we're degenerating and that this degeneration is the result of our failure to be religious, or more properly our failure to be religious in the sense that our fathers and mothers reputedly were. That is to say, our failure to be Christian enough here in the West, and apparently our failure to be Muslim enough elsewhere.
Christians of a historical bent may feel somewhat uncomfortable in taking this position. They may recall that Christianity was once perceived as a depraved oriental cult and that its prevalence was said to be the reason for the fall of the Roman Empire, as late as Gibbon but especially during the fall of the empire. The early Church Fathers spent a significant portion of their energies denying that Rome must return to worship of traditional pagan deities in order to retain its glory. Some cynical souls may speculate that the Church's incorporation of many aspects of pagan religions was motivated by a desire to placate the feelings of those who felt that abandoning the old ways was wrong, and harmful.
Must one be religious--in particular traditionally religious--in order to be moral, to live an ethical life? I don't see how this proposition can be maintained. Even the religious have been known to admit now and then, perhaps grudgingly, that atheists have lived highly moral lives. Christian morality may be different in some respects from pagan morality, but pagan philosophers, Platonic, Aristotelian, Stoic, Cynic and even Epicurean championed high moral standards and had no need to rely on the very personal God of Christianity in order to do so. This has even been acknowledged by Christians--think of Dante placing the great pagan philosophers rather comfortably in the first circle of hell; they were not deserving of the horrors he delighted in visiting on other citizens of that place, many of whom were Christian.
If the pagan philosophers managed to promulgate high moral standards without recourse to "religion" as organized religions conceive it, it would seem it's very possible to do so, and even to live by those standards, without religion as such. Why then are we so frequently being told otherwise?
Some may maintain that one must at least believe in some kind of law-giver God in order to be moral, but that doesn't seem to work, either, nor does it seem that some kind of creator God is required. Certainly systems of morality were derived in the past and are still derived from the belief in natural laws, or the wisdom of living in accordance with nature. But these systems are justified based on nature itself; they don't necessarily require that nature have been specifically created by a God for some purpose.
So perhaps it isn't necessary to be religious to be moral. It's simply necessary to be moral, and morality isn't necessarily grounded in what most believe to be religion, although it may be grounded in wisdom. Those who claim we must "return" to religion, and especially a certain kind of religion, to save ourselves from depravity may therefore do so because they think that most of us can't be wise if left to ourselves, or because they feel a certain religion is exclusively true, or for other reasons which aren't all that compelling or honorable.