Deliberate exclusion IS bullying by every accepted school definition.
Only to a point. As an example defnition: "Social Exclusion is now recognized as a sub group of bullying. This means that idea of excluding someone repeatedly, aggressively and on purpose with the intent to cause emotional harm to them, is right up there with verbal, physical and cyber bullying." (source)
That seems miles away from "if you let one kid join an activity you must let any kid join".
Certainly "you can't play with us because you're (insert protected class here - gender, religion, skin color, etc.)" is problematic. But that's very different from "you can't play with us because last time you kept stealing the ball". Context matters.