I think beliefs are different though. We aren’t born with them, we develop them and they change over time - wouldn’t an identity based exclusively on belief be either unstable or dangerous?
For example, if you believe that something is sacred or important and it’s shown and proved to be worldly and dull, wouldn’t that unhinge a person as much as a loss of position or ability? I suppose it maps better if belief is in a single object or person, sure. But what if you change your mind?
Or worse, what if you can’t change your mind and want to, because you don’t want to let go?