Implicit atheism is still concerned with not believing in religion.
The way I see atheism is that a belief in no religion is, by its nature, a religion. Joe is a christian and believes in Jesus, Bob is an atheist and believes no god; both are merely two sides of the same coin. You can't call yourself non-religious if you believe in a religion, whatever the specific form.
Being non-religious means you don't care; it's not that you don't believe, you simply could not care less one way or another. Wikipedia appears to call it apatheism[1] and more broadly irreligion[2], but semantics aren't the focal issue here.
