So maybe instead of nature based, the term should be nature worship?
I think the problem with that is that it leads into "you don't worship the *gods*, you worship nature." While some folks certainly do worship some kind of abstract "nature," there are a number of people who worship gods that are explicitly, intimately connected with nature, and whose religious practices center around a celebration of the natural cycle, rather than, like "nature itself." "Nature worship" is reductive, and also excludes most of the folks usually understood -- by themselves and others -- as nature-based.