This post is not to be taken as a doctrine of intolerance, but of historical and intellectual honesty.
By definition, Pagan is either someone who believes in the old Pagan Gods, or who worships nature, and therefore recognizes the conscious Divinity of the natural world and universe. Therefore, it would be impossible for an atheist to be a Pagan because Pagans acknowledge Divinity. Atheists do not believe in any form of God, Gods or conscious Divinity. I think the atheist community as whole would agree on that. That's why they're called atheists. It is A-theism, which means an absence of theism. Whereas Pagans believe in Gods or Divinity, which makes them theists. If you believe in a God, Gods, or Divinity, then you are NOT an atheist. You can call yourself a theist; it's ok. It's not a bad thing.
I think many people have confused the adoption of Pagan elements with an inherent constitution of Paganism, such as environmentalism, humanism, and a love for mythology. Pagans are most certainly environmentalists, humanists and mythologists, but just because you love nature, humanity and myth, doesn't necessarily make you a Pagan. No more than admiring Jesus makes you a Christian, or thinking parts of the Torah are beautiful makes you a Jew, or loving India makes you a Hindu. I am sure there are many Christians who enjoy Pagan myth and history as a study, and who are environmentalists and humanists, but that doesn't mean they're Pagans and not Christians. Just because you adopt elements of something, doesn't make you part of the larger whole. Barack Obama is an environmentalist, but still a general Christian. George Galloway is a humanist, but still a Catholic (some claim he's actually converted to Islam). My father-in-law has books on Norse mythology, but he's still an Episcopalian.
Never in all of my life have I heard of a Pagan culture that was atheist. Never in all of my years of study have I read any reputable Pagan material, either from modern or ancient authors, that does not talk about Gods and Goddesses or Divinity. Therefore, the Atheistic Paganism movement is an attempt to redefine what it means to be Pagan, and what it has always meant since the times of ancient.
I'm quite a liberal person, but there has to be standards when known identities are concerned, otherwise the Pagan movement is going to become so skewed that it won't know who it is anymore or where it's going. We have to have at least some basic structure. If you don't want to be Pagan, then don't be Pagan. But don't call yourself Pagan if you're not going to adhere to the structure that Paganism has always had since its first days on this planet, and that it still retains as a whole community.
In the Goodness of the Gods,