The phrase 'atheist religion' may seem like an oxymoron, but many would apply it to Buddhism. The term ‘atheist’ refers to any individual or body of thought that denies or disbelieves in the existence of a supreme being, creator, or deity. By this definition, Buddhism is an atheist philosophy, as it posits no God or supreme deity. The Buddha was a man, not a god, who awakened to the way out of suffering, and developed teachings to help others do so too.
As Stephen Batchelor, author of Confessions of a Buddhist Atheist, puts it in that book:
"The Four Noble Truths are pragmatic rather than dogmatic. They suggest a course of action to be followed rather than a set of dogmas to be believed. The four truths are prescriptions for behavior rather than descriptions of reality. The Buddha compares himself to a doctor who offers a course of therapeutic treatment to heal one's ills. To embark on such a therapy is not designed to bring one any closer to 'the Truth' but to enable one's life to flourish here and now, hopefully leaving a legacy that will continue to have beneficial repercussions after one’s death."
Few Buddhists would disagree with this characterization, and yet Buddhism is classified as a religion by sociologists and historians, and in fact is usually considered one of the world's five major religions. Some branches of Buddhism have all the 'trappings' of other organized religions, including temples, priests, iconography, and both lay and monastic practitioners.
In addition, Buddha statues and paintings are prevalent, and rituals and offerings appear to be directed towards him as if he is a god. In some branches of Buddhism, particularly Tibetan Buddhism, similar rituals and prayers are directed towards other Buddhas, dakinis, and deities that appear to be worship-like in nature.
Some Theravada Buddhists believe these kinds of practices are in fact against the Buddha's teachings, as he himself said 'do not worship me' and 'he honors me best who practices my teaching best.' However, rituals and practices that appear to worship the Buddha are really about paying respect and practicing reverence for the Buddha's awakening. Deity practice is about recognizing the traits and 'enlightened mind' represented by these beings, and about recognizing these as also residing within ourselves. They are symbols and tools for recognizing our own innate Buddha-mind, and are meant to break down the distinction between ourselves and Buddha, as opposed to placing him above us, as with a god.
Because of the atheist nature of Buddhism, some people practice it in combination with other religions, particularly in the West. The Dalai Lama, the Tibetan spiritual leader, has in fact spoken of this trend, and when asked if it is OK to practice both Buddhism and another religion, has said that he believes it is, particularly when one is in the early stages of the spiritual quest. In Imagine All the People: A Conversation with the Dalai Lama on Money, Politics, and Life as it Could Be he says, "It is like being in school: as long as you remain at the general level, you may study a range of subjects."
However, he goes on to say that as one "goes deeper into Buddhist practice, which is based on voidness, interdependence, and no absolute, there is no place for belief in a creator." At some point, one must make a choice.
In Buddhism, we are not asked to make this choice based on belief or someone else's say so. We are urged to seek the answer for ourselves, through meditation, inquiry, and mindfulness – all forms of studying our own mind and through this the nature of reality. If through this practice, our experience is one of 'voidness, interdependence, and no absolute' (or the Three Marks of Existence, anicca, dukkha, and anatta) then it stops being a matter of choice, and is simply what we have realized for ourselves.
This leaves a lot of space for different kinds of practice within Buddhism, and this has caused disagreement between sects at times, although in general much less than in other religious traditions. The concept of 'upaya' or 'skillful means' also plays a role in the understanding of belief or faith within Buddhism - while we may be asked to provisionally accept the doctrine of rebirth and other teachings, ultimately our acceptance of them is meant to arise from our own practice, not out of a blind acceptance of dogma.
The bottom line is that Buddhism is many things to many people. Whether or not it should be called an 'atheist religion' depends on the perspective one is viewing it from.