One of the blanket terms for Neopagan traditions is "nature-based." This is a label which many reconstructionist pagans reject for our traditions. Yes, our calendar of feast days is related to natural events, and the lore from which we draw inspiration for our practices is rife with tales of nature interactions as told through the bonds and wars amongst our gods. But frankly, claiming a reconstructionist pagan is practicing a nature-based religion is not presenting the entire picture.
A nature-based religion in and of itself requires no relationship to a culture other than some passing nod to the majority secular one of the nation in which the practitioner resides. A subculture within it, to be sure, but there's nothing barring a nature-based pagan from developing a practice that bears the names of gods not followed at any time in Europe or any other nation. As a reconstructionist, the standards are a bit different. And what those standards encompass is more than the cycles of the moon and sun.
Not only are we seeking to build a religion that's sensitive to the cycles of the natural world, we're working out how to do this within a specific cultural framework. This is why many of us prefer the term "culture-based" paganism over "nature-based." The relationship to nature is part of the culture and cannot be removed from it without significant difficulty. There's something to contemplate in a culture such as the Celtic set, in which a god established a holiday in honor of a goddess who clear-cut a forest to permit grain to grow and died from the effort. How do we square that with many of the minimal-impact philosophies bandied about in environmental circles? Do we curse our ancestors for their cruelty or recognize it as a sign that it is impossible to live on the earth without affecting it and choose how to do so instead? And how would our ancestors have felt about it then? How do the modern members of that culture square it in their heads? These questions are just one example of the wider set contained in determining and practicing a culturally sound approach to nature interactions.
We also do not worship nature per se. Forget all of the jokes about druids and trees; they were part of a symbolic complex, not the end-all of the lore. Natural events, the gods, the ancestors and the spirits that dwell within and without the world at the same time all combine into one dynamic system that informs the culture and is interpreted by it at the same time.
Nature is, thus, part but not all. It's impossible to split them, so labeling something with part of the whole just doesn't make sense to me.