The New Statesman asked several famous people about what atheists could learn from religious believers, here.  Particularly interesting were the responses of Francis Spufford and Karen Armstrong. 
Spufford:

When Thomas Paine was dying in Greenwich Village in June 1809, two Presbyterian ministers popped by to suggest that he would be damned if he didn’t affirm his faith in Jesus Christ. “Let me have none of your popish stuff,” he said firmly. “Good morning.” Score one to Paine for exiting the world without compromising his convictions, yet what he said had made, on the face of it, no sense.
Faith in Christ as the path to salvation isn’t “popish” in the sense of being particular to Roman Catholicism. Paine was speaking to a pair of impeccable Protestants. What he was doing here was to act as a very early adopter of a perception that would influence later atheist understandings of the world enormously. He was suggesting, in one charged and revealing insult, that the original Protestant critique of Catholicism should be extended to the whole of historic Christianity. All of it should be reformed away; all of it, absolutely all of it, deserved the contempt that zealous Puritans had once felt for indulgences and prayer beads and “priestcraft”.
This post-Christian puritanism, largely oblivious now of its history, is highly visible in the New Atheism of the 1990s and 2000s, and especially in Richard Dawkins’s The God Delusion. Strange indifference (except at the margins) to all religions except Christianity? Check. Sense of being locked in righteous combat with the powers of darkness? Check. Puritanism, it turns out, can float free of faith and still preserve a vehement world-view, a core of characteristic judgements. The world, it says, is afflicted by a layer of corrupting gunk, a gluey mass of lies and mistakes that purports to offer mediation between us and meaning but actually obscures it and hides the plain outlines of that truth we so urgently need. Moreover, this hiding, this obscuring, is wilful and culpable, maintained on purpose for the benefit of hierarchs, bullies, men in golden hats everywhere. It is our duty to take up the wire wool of reason and to scrub, scrub, scrub the lies away. For no mediation is necessary. We may have –we must have – a direct vision of the essential state of things. We must see the world as if through pure, clear water, or empty air.
It is reassuring, in a way, to find this ancient continuity at work in the sensibility of Dawkins, Sam Harris, Daniel Dennett and Jerry Coyne. It kind of makes up for their willed ignorance of all the emotional and intellectual structures of faith (as opposed to the will-o’-the-wisp “popery” in their heads). Dawkins may be showing indifference to every word ever written about the differences between polytheism and monotheism when he declares that Yahweh is the same as Odin, and that all he wants “is one god less” – but he is also keeping up a 400-year-old campaign against idolatry. That distant sound you hear is Oliver Cromwell applauding.
However, the project is impossible – as impossible for the New Atheists as for every previous builder of a purified New Jerusalem. Direct, unmediated apprehension of truth is not available, except in the effortful special case of science. That gunk the New Atheists scrub at so assiduously is the inevitable matter of human culture, of imagination. People secrete it, necessarily, faster than it can be removed. Metaphors solidify into stories wherever the reformers’ backs are turned. We’ll never arrive at the Year Zero where everything means only what science says it should. Religion being a thing that humans as a species do continuously, it seems unlikely that we’ll stop, any more than we’ll stop making music, laws, poetry or non-utilitarian clothes to wear. Imagination grows as fast as bamboo in the rain. The world cannot be disenchanted. Even advocacy for disenchantment becomes, inexorably, comically, an enchantment of its own, with prophets, with heresies and with its own pious mythography.
I think our recent, tentative turn away from the burning simplicities of The God Delusion (and the like) represents a recognition of this. Alain de Botton’s discovery in religion of virtues and beauties that an atheist might want is an anti-puritan move, a reconciliation of unbelief with the sprouting, curling, twining fecundity of culture. I don’t expect the puritan call will lose its appeal to the young and the zealous, but maybe we are entering a phase of greater tolerance in which, having abandoned the impossible task of trying to abolish religion, atheists might be able to apply themselves to the rather more useful task of distinguishing between kinds that want to damn you and kinds that don’t.”

Armstrong:

Most of us are introduced to God at about the same time as we hear about Santa Claus, but over the years our views of Santa mature and change, while our notion of God often gets stuck at an infantile level.
As a result, “God” becomes incredible. Despite our scientific and technological brilliance, our religious thinking in the west is often remarkably undeveloped, even primitive, and would make Maimonides and Aquinas turn in their graves. They both insisted that God was not another being and that you could not even say that He (ridiculous pronoun!) existed, because our experience of existence is too limited. God, said Aquinas, is Being itself (esse se ipsum).
The biblical God is a “starter kit”; if we have the inclination and ability, we are meant to move on. Throughout history, however, many people have been content with a personalized deity, yet not because they “believed” in it but because they learned to behave – ritually and ethically – in a way that made it a reality. Religion is a form of practical knowledge, like driving or dancing. You cannot learn to drive by reading the car manual or the Highway Code; you have to get into the vehicle and learn to manipulate the brakes. The rules of a board game sound obscure and dull until you start to play, and then everything falls into place. There are some things that can be learned only by constant, dedicated practice. You may learn to jump higher and with more grace than seems humanly possible or to dance with unearthly beauty. Some of these activities bring indescribable joy –what the Greeks called ekstasis, a “stepping outside” the norm.
Religion, too, is a practical discipline in which we learn new capacities of mind and heart. Like premodern philosophy, it was not the quest for an abstract truth but a practical way of life. Usually religion is about doing things and it is hard work. Classical yoga was not an aerobic exercise but a full-time job, in which a practitioner learned to transcend the ego that impeded the ekstasis of enlightenment. The five “pillars” or essential practices of Islam are all activities: prayer, pilgrimage, almsgiving, fasting and a continual giving of “witness” (shahada) in everything you do that God (not the “gods” of ambition and selfishness) is your chief priority.
The same was once true of Christianity. The Trinity was not a “mystery” because it was irrational mumbo-jumbo. It was an “initiation” (musterion), which introduced Greek-speaking early Christians to a new way of thinking about the divine, a meditative exercise in which the mind swung in a disciplined way from what you thought you knew about God to the ineffable reality. If performed correctly it led to ekstasis. As Gregory of Nazianzus (329-90) explained to his Christian initiates: “My eyes are filled and the greater part of what I am thinking escapes me.” Trinity was, therefore, an activity rather than a metaphysical truth in which one credulously “believed”. It is probably because most western Christians have not been instructed in this exercise that the Trinity remains pointless, incomprehensible, and even absurd.
If you don’t do religion, you don’t get it. In the modern period, however, we have turned faith into a head-trip. Originally, the English word “belief”, like the Greek pistis and the Latin credo, meant “commitment”. When Jesus asked his followers to have “faith”, he was not asking them to accept him blindly as the Second Person of the Trinity (an idea he would have found puzzling). Instead, he was asking his disciples to give all they had to the poor, live rough and work selflessly for the coming of a kingdom in which rich and poor would sit together at the same table.
“Credo ut intellegam – I commit myself in order that I may understand,” said Saint Anselm (1033-1109). In the late 17th century, the English word “belief” changed its meaning and became the intellectual acceptance of a somewhat dubious proposition. Religious people now think that they have to “believe” a set of incomprehensible doctrines before embarking on a religious way of life. This makes no sense. On the contrary, faith demands a disciplined and practical transcendence of egotism, a “stepping outside” the self which brings intimations of transcendent meaning that makes sense of our flawed and tragic world.”