Roes now you have typed that. go back and read it again!
You start of well, gender and sex as 2 discrete articles. Well done!
Then, well, naturally the real and acknowledged distress a trans person feels is sll down to us non trans, misgendering. No... really, it isn't, as any trans individual will tell you, the distress a trans individual feels is dismorphia, not name calling!
And al that binding and 'trying to pass' that is also dismorphia!
And then you really make that leap: they still will have genitalia and secondary sex characteristics of their biological sex, so many trans people undergo surgery to change it.
Yes, they change the physical manifestation of their biology. They cannot change their biology!
HTH 