There are plenty of horribly unhealthy societies with, or based upon religious faith. I'm also not a student of history, but I think that the ancient Greeks were barely religious (in the modern sense of the word). They had a religion, but I'm not sure it provided much in the way of moral guidance. (Please correct me if necessary).
Let's just draw this out to logical conclusion for a moment. Polytheistic religions almost NEVER provide a moral compass. They explain why stuff works the way it does and say if you pray to the Rain God your crops will grow better. As societies evolved beyond their basic, "beat a living out of the Earth existance," and had time for art, engineering and philosophy, they tended to start ignoring their own Polytheism. Why? It provided them nothing. Want your crops to grow? Build a friggin aqueduct... Is that morality?
The Big Book Religions. More or less these are big clubs you join, which along with membership dues may demand or suggest a certain style of living in order to "get to heaven." By contrast, all polytheists go to heaven (or hell). This is morality: "Da Rules."
I don't know much about Hinduism except that it is somewhat polytheistic, pantheistic, and monotheistic all at the same time. Very '60s... Karma matters, but only because you can never leave the cycle (reincarnation). You lead a good life NOT because the rules says so but just because that just happens to be how the Univerise is constructed. Is that morality?
Buddhism? Buddhism is about figureing crap out to make YOU happy and centered. Live this way because you will be at peace with yourself... Is that morality? (Enter Confuscius)
From Merriam-Webstser:
1 a: a moral discourse, statement, or lesson b: a literary or other imaginative work teaching a moral lesson
2 a: a doctrine or system of moral conduct bplural : particular moral principles or rules of conduct
3: conformity to ideals of right human conduct
4: moral conduct : virtue
But let's look at entry 4 momentarily as well. Virtue? Virtues are culturally subjective and vary quite widely.
That all being said,
Humans require religion; it is NOT going away anytime soon. That's not a judgement, it just is. Way I see it, some of us happen to be wired in such a way that we either don't need it, or can't accept it at all, like an allergy. But for most of us, it is a critical component to our lives and our cultures.
Morality, on the other hand, is probably one of the murkiest terms out there and I'm not so sure it has anything to do with good, noble, or sustainable society.