You know, you can just say "supernaturalism" instead of "religion". The two are not synonymous. You can have religion without supernaturalism, such as non-theistic Satanism and some forms of Buddhism. You can have supernaturalism without religion, which describes many New-Agers. I'm sure you've heard people say "I'm spiritual, but not religious", and that's what they mean by that. There are people who believe in souls and reincarnation and stuff like that, but they don't have a religion built around it.

In the case of non-theistic Satanism, there is a moral code, a set of beliefs, and a community of people with shared values, as well as holidays and rituals. Just nothing supernatural.