Ultimately, it might not matter to any of us. Everyone is free to like what they like, believe what they believe, and even pretend to be something else. Do I care that Sally became Sal next door? Not really. But I kind of care if Sal tries to say "she's" the same as me. "She" is not.
And even more true the other way around. I as a man, can certainly pretend to be a woman, and even think of myself as a woman.. but how can I ever stare a real woman in the face and pretend to know what she has gone through? I don't menstruate. I didn't go through different forms of puberty. I don't make less than the average male. How offensive is it then, for a guy to say to a woman that he "knows what it's like". They don't.
And further, where does this stop. I see trans-autistic is now a thing. I thought I was black up until I was 18. Do I now have not only the right to claim African-American as my race but also expect the black communities to accept me?
At the end of the day, you are what you are. You can be a female, who shares every interest that men have.. nothing wrong with that. But you're still a female. Society can't continue to let people just claim things they aren't. Does a poor person have the right to say "Na I'm rich now" and just go rob someone? Where does it end.