Do you really not get this yet: you don't know what the concept of identity actually is.
Repeated insistence doesn't make your superficial approach to identity any more compelling.
The shape of the tree is not the analogy for identity, the shadow is.
I know that was your intention; the fact you chose the distorted, mutable image rather than the actual object as definitive of "identity" is precisely the issue.
Your identity isn't your self-image, it's not a list of your traits, it is the things that distinguish you from or associate you with others. Distinguishing and associating are things that happen based on projection and perception, identity is based in those things, it is not just "what exists".
Distinguishing and associating are not simply a result of superficial external perceptions, divorced from the characteristics of the object itself-- they are ultimately derived from the traits and characteristics of the object.
So the process of 'identifying' someone or something requires an external observer and their interpretation. Yet, the only tenable and reliable basis for it rests in the characteristics of the object, not solely the eye of the beholder. Rely solely on the latter and ignore the former, and you'll constantly be making unworkable assumptions and foolish mistakes.
It's like "gender expression" is not a question of who you are, it's explicitly expression, it is a communicative concept. That expression helps shape identity by influencing the perception of others that will then associate or distinguish you from other people and things.
Again, completely at odds with what you said before, that men and women need not act or look according to the stereotypes and expectations of their sexes, and that they would remain men and women.
Now you're pushing a standard by which if someone is biologically male, and identifies as a male, but presents according to modern stereotypes of femininity and is mistaken for a woman by an observer-- that's now their identity! To hell with their actual characteristics, eh?