Gender identity is real but not universally felt. Like religion. Not everyone has one.
The analogy with religion is a good one actually.
I have a friend who is fairly staunchly Christian, believes in God, after life, the whole thing. She prays, sometimes says she prays for me, she goes to church every Sunday, she reads and believes bits of the Bible.
I don't believe any of it I think it's bullshit. I don't really understand how she can believe it. She might even be quite upset if she knew how ridiculous I thought it was. But I don't say that to her. I let her get on with her life and she let's me get on with mine. Because what she does has no bearing on me.
However, if she suddenly started telling me that I had to believe in God, forced me to start praying, gave me mantras that I had to repeat, made me go to church, and expected me to to change my life to fit her beliefs, then very quickly I would say something. I might start by saying that she has no right to make me redefine who I am to fit her beliefs.
But if she persisted, then it probably wouldn't take me very long to lose it with her and shout at her 'why the fuck do you believe in something so completely and utterly ludicrous and untrue? I have been humouring you because you weren't hurting me, but enough is enough, I don't believe this bollocks and you have no right to make me bend to your beliefs. RELIGION IS BULLSHIT, SORRY IF THAT HURTS YOUR FEELINGS BUT I DON'T CARE. '