This is not limited to California. There are a number of US states where an unincorporated association is a legal person. There are also other types of legal persons that can be formed without incorporation, such as partnerships and trusts. So the etymology is not dispositive.
Common law is also a bit of a misnomer as used here. Although the US is a "common law" country, we have miles and miles of statutes, codes and regulations (federal, state and local) that make up our laws. There are underlying principles and defaults that come from "common law," but finding these in their natural state in the law is about as likely as finding an old growth forest in Manhattan. As I understand it, the more relevant distinction between common law and civil law, in action, is that under common law, judicial decisions create binding precedent that dictate how the statute must be interpreted (a gross oversimplification), while civil law maintains the primacy of the statutory text (plus any regulatory overlay, etc.)
It may be the case in other common law jurisdictions that unincorporated associations have been granted legal personhood, though I'm not sure that's relevant. What's more relevant is that under principles of comity and other international law principles, the personhood of an entity in its state of domicile will generally be respected in other jurisdictions. US courts don't turn away GmbH and SpA entities, for instance, even though they aren't the same as US entity types. Similarly, the UA form should not be disregarded in a foreign jurisdiction that does not itself view UAs as legal persons.
Greg