Living a life is a matter of making risky decisions. For almost all of them we can use the theory of subjective expected utility. That is we have a sense of what we want to achieve and a sense of how likely different bets are to achieve that and we take the bet that is most likely to get us what we want.
But for some decisions that approach won’t work. The most dramatic are ones where we actually could die. So the Nazis come and ask you to collaborate or be killed. There’s no obvious way to use SEU to answer this question because on one of the prongs of the decision tree you won’t be there any more.
That’s a dramatic example but there are less dramatic ones all the time. Ones about how to live my whole life, and ones where on one fork of the decision tree I’m a different kind of person where different things are important to me. Anything where the bet I make affects who I am in a deep sense, i.e. where I’m not just fulfilling my preferences but acting in a way that will affect what my preferences will be from here on in. Religion is the realm where we deal with these kind of decisions.
A consequence of this definition is that religion is not about statements about reality — God exists, God doesn’t exist, there is an afterlife, there is not an afterlife — or only about such statements insofar as they cause us to engage with these ultimate risks in a particular way. So for example — “the world might end tomorrow” — might in the mouth of a certain type of messianist be a religious message. Or it might not.
We might want to put statements of belief in a bundle of other religious practices — rituals, community-building exercises, art — that help us maintain a particular attitude towards risk. And if that’s right then these are all secondary. It’s the attitude towards risk that makes a particular practice religious, not the practice itself.
Another consequence of this definition might be that everyone is religious, some people just don’t know it. Whether that’s a welcome consequence, or whether it would be better just to check the language of religion, I couldn’t say.