All societies are religious. Therefore, atheism always involves, not only the acceptance of a certain worldview, but the rejection of a certain ancestral religion. In fact, “rejection of religion” defines atheism much better than does “absence of religion.” (William Lane Craig often points out that his pet cat’s lack of belief in God does not make his pet cat an atheist—an atheist, unlike Craig’s pet cat, does not just lack a certain belief, namely that there is a God; he also has a certain belief, namely that there is no God.) The relationship between the atheist and the ancestral religion he rejects is often quite complicated. Because the atheist has grown up in a culture saturated by that religion, the biggest influence on his ideas is usually—that religion. Thus, we can talk about pagan atheists, Christian atheists, Jewish atheists, and so forth, observing, e.g., that Jewish atheists are more ethnocentric than Christian atheists because Judaism is more ethnocentric than Christianity.
I know very little about what non-Christian atheists are like. Since I live and have grown up in a culture that is still vestigially, culturally Christian, all the atheists I have met have been Christian atheists. I used to be one myself. Like the Christian, the Christian atheist has a linear and teleological view of human history, which he sees as an inorexable march towards a “scientific” civilization free of all the superstitions of old. Like the Christian, he is a universalist who holds his beliefs to be equally true and important for every person and every nation in the world—and like the Christian, he therefore proselytizes.
We can also talk about denominations of Christian atheism—about Catholic and Protestant atheists. (As might be expected, Orthodox atheists have a great deal in common with Catholic atheists.)
The natural habitat of the Protestant atheist is, not surprisingly, Northwestern Europe and North America. He has at least two distinguishing traits. Firstly, he likes to use secularized versions of the Protestant Reformers’ attacks on the Catholic Church against all of Christianity (or rather “religion” or “organized religion,” which is usually code for Christianity), condemning it for being corrupt, authoritarian, Medieval, and Pharisaical. Secondly, he is glibly dismissive of Protestantism, but hates the Catholic Church with a boundless, fiery passion. “New Atheists” like Richard Dawkins are Protestant atheists through and through.
The Catholic or Orthodox atheist, on the other hand, thirsts for a hierarchical and infallible institution to replace the one he has left. In practice, this tends to be a political movement of some sort, usually Communism. The Party is his Church, and the Chairman his Pope or Patriarch. This may be one reason why Western European Communist parties have been largest in Catholic countries like Italy or France, and why Communism has been even more successful (if that’s the right word) in the Orthodox East and in Catholic Central Europe.
Can the comparison be stretched too far? Sure. Few Christians–I was going to write “no Christian,” but thought it best not to annoy the Anglo-Catholics–are both Protestant and Catholic, but just as few Christian atheists are purely Protestant or purely Catholic. Catholic atheism and Protestant atheism are like liberalism and leftism in this regard–it’s theoretically useful to separate them, but you rarely, if ever, see a pure specimen of either in the wild.