I'm not sure nationalities are a good comparison. It is possible to change nationality. It isn't possible to change sex.Your sex isn't something you 'identify as' it is something you are, and would be even if you were severely disabled and unable to verbalise at all.
You can, to a point. In so much as we've abstracted it to be a bit of paper. But can you really take a Frenchman and make him something else, or will he always, in a sense, be a Frenchman?
Your sex is what you are, but we all I think take on certain kinds of awareness and looking at ourselves in a certain way, our sense of belonging to a particular group. If you have a sense of solidarity with other women, that's something different than just having a sexed body, for example.
We seem to have a significant capacity for creating identity with all kinds of different groups, based on biology or other things.
I think this is a capacity that's become a little weird in recent years, so maybe that feeds into this idea that a change in our sense of identity should mean we recognise some more basic change.