It’s true that I’m only familiar with two country’s legal systems (and both are common law jurisdictions), but as I understand it, your “legal gender” in the UK is only well-defined if you acquire a GRC, which is something only trans people do, and plain old doesn’t exist in the US. (To be fair, I imagine if you brought a discrimination case on the basis of gender in the UK your gender might be established as a result, but among the long list of things I am not is an attorney (anywhere, never mind in one of the UK’s multiple legal systems).)

Amusing, the letter that comes with the GRC asserts that it should suffice to establish your gender for any interested entities, which is decidedly false overseas.