Both, religion and atheism are just a state of mind, so moralism that stems from them must also be a state of mind. The simple proof to this is the fact that different religions, as well as different atheistic views have different codes of morality. In other words, it's up for grabs what we choose to define as "moral."
Being a subjective matter, neither religion nor atheism are "right" or "wrong". There is, however, this little matter of human intellectual arrogance, so each side may claim to hold the bag with truth. Both have developed highly elaborate, suggestive, and often intimidating "belief systems" - as one is using fear as its tool, and the other is using "sanity, common sense", "objectivity" (whatever that is).
The simple fact about human nature is that we'll have to wait for a little longer in our evolution, so that the primordial, primitive, and animalistic part of our brain loses its dominance over our more altruistic, moral, advanced frontal lobe. It may not appear so obvious, but it's actually the basic problem in our morality. Our lower brain is about survival instinct, (territoriality), hoarding of the means of survival, (greed), procreation (sex), and fear (power and wars).
When I say "evolution", I mean evolution of consciousness. It's a fact that our thoughts, attitudes, and beliefs affect structural changes in our brain, something known as "neuroplasticity". I don't want to sound too prophetic, but the time may come that our collective conscious effort in a positive direction weakens the dominance of primordial brain, and altruistically based morality becomes our automatic nature.
Until then, the fear of unknown (generated by primitive brain) will keep producing religious beliefs, insecurities compensated by hoarding, territoriality, and a need for dominance. Our most cherished illusions of coexistence - like patriotism, American Way, success, ambition - will lose their primitive drive, and folks will come to terms with their differences, individuality, uniqueness as their mental fingerprint. Mutual support instead of competition will be the norm.
At the present state, it's useless to be religious, because we are not "wired" to follow any enlightening teachings (except for some advanced individuals). We live switched on automatic pilot, which means living unconscious, driven by animalistic urges.
So, both religious and atheistic morality will have to change with our level of awakened consciousness.