I found the article on Atheopaganism fascinating. I'm glad someone is organizing something like this. I have similar leanings myself, although my sensibilities rebel against the rituals and observances.
My guess is that, before someone officially finds out that he or she is an Atheopagan, that person calls him/herself "spiritual, not religious". But I don't think I've ever put myself in that category because I can not believe in any spiritual entity.
However, I have such a deep..... is "connection" the right word?....with nature. Maybe that's not right, "appreciation and gratefulness" may be better. But whatever the word is, nature feeds me, the stars, the moon, the trees, dirt, sunshine, rain, birds, animals, mushrooms, seasons, it all feeds my soul and makes me feel whole and satisfied and peaceful. So I understand this belief system, i just couldn't participate in the whole thing. Because I would hate to offend someone by giggling and feeling stupid hailing the moon or whatever.