These labels are all fuzzy, so self identification is the only reliable way of applying labels in any sense. For example, if the Chinese communist party says they are communist, why would you want to argue with them?
True
> so self identification is the only reliable way of applying labels in any sense
No, it's not. Self-identification is one of many ways of operationalizing a categorization, and it's useful for some purposes but not others. You can also operationalize by sets of concrete policies, which is useful for different purposes. And there are other options.
The relevant basis of categorization depends on the purpose of categorization.