I agree that one of the major reasons the 'nature-based' discussions often become more of an arguement is because there isn't a set definition of what 'nature-based' actually means. If one person decides that their religion is nature-based, and they meet another person and find out that they have the same religious beliefs as them, then they may well come out with: 'hey, your religion is nature-based too!'. But the other person disagrees: he/she has never identified themselves like that.
A big part of the definition problem, in my opinion, is what the 'based' part of 'nature-based' actually stands for. For instance, if a drink label says that it is 'water-based', what does that mean? Does it mean that water is the main ingredient and everything else is insignificant? Or is there just slightly more water in it than anything else, but the other ingredients are also an important part of the drink? And what are the other ingredients? Are they different ingredients to another drink that identifies itself as water-based?
I know that was a rather silly analogy, but it's all I could come up with at this time.
Actually it's a great analogy. If you say something is water based, then you assume it has water with other things added. So if you say nature based, should we assume that the religion starts with being about nature and has other things added? That nature is the 'basis' for the religion?
Of course, I have trouble with earth-centered too. Because everyone on this board is assumed to be on the planet Earth. Kind of hard NOT to have it figure in our lives and our religions if only as the place we are right now! But that doesn't assume that earth worship is part of any given religion.
So maybe instead of nature based, the term should be nature worship?