In theory, join(a, b) should always give the same result as join(b, a) (permutation invariance). However, this is not always the case. One example I found is the following (related to the testAbstractTypeInADict unit test)

https://mypy-play.net/?mypy=1.17.0&python=3.12&gist=e4df640a72c4f61c1a33a50db60fd6e5

class Class: ...

def join[T](x: T, y: T) -> T: ...

klass: type[Class]

reveal_type(klass)  # N: Revealed type is "type[__main__.Class]"
reveal_type(Class)  # N: "def () -> __main__.Class"

reveal_type(join(klass, Class))  # N: Revealed type is "builtins.type"
reveal_type(join(Class, klass))  # N: Revealed type is "builtins.object"

Moreover, when debugging this, mypy actually evaluates both is_subtype(left, right) and is_subtype(right, left) to true.