ok.
Still thinking about the sense of self thing, but again, coming at the thing from just where I am in my pathway through all this. I'm aware people will disagree, and they're welcome to, i dont claim to have all the answers.
This whole thing is difficult, i mean, i'm a woman, my sense of my gender identity matches my biological sex and always have. I'm a Trans Ally and also a staunch Feminist, and even i have some disconnects between those two parts of myself so am often puzzling through questions myself.. the nearest similarity of lived experience i can come up with was when i was studying philosophy as a christian and began questioning my religious faith (i came out of that one as Pagan.. so... yeah. 
) its never easy.
Its HARD to have a discussion and answer 'what is a woman' without falling into the trap of using stereotypes that as a feminist i absolutely detest, however, i reason it out that its the world I grew up in that is to blame there.. we grow up having 'this is female' and 'this is male' pounded into us by our parents, schools, grown ups, society, from a time when sex/gender were the same thing to the overwhelming majority of people.
We've had our head stuffed full of stereotypes on what makes a woman, and what makes a man from the word go.. so as the situation and world evolves around us, are lacking the language and experience to explain what 'woman' and 'man' is without using that language and accepted stereotypes that we've grown up with.
I wish i could find the words to say what is its about me that makes me go 'yes i am a woman' beyond my chromosomes, genitalia and identity, but i can't.. and i also can't explain WHY someone else feels a disconnect between their biological sex and gender, because i've never personally experienced it.
All i can do is have empathy, and try to understand that they obviously feel, for whatever reason, that their sense of self doesn't match their outward biological appearance, and be accepting of that, to use their preferred pronouns, their new names, while i muddle through some of my own thoughts and feelings on it.
I'm happy to share bathroom space with a transwoman, but i'm also aware some people aren't.
I have difficulty accepting transwomen in biological womens sport, because i can see/understand the science on how our physical chromosomal make up gives biologically male bodies an advantage.. but i can also understand the upset for someone who doesn't FEEL male in any way shape or form.
I have no issue in the use of inclusive language around childbirth because i personally don't feel that words can erode my womanhood or my identity.. but i CAN see some of the arguments about the erosion of 'woman' for some people.
I dont have the answers, for me i just work on the ideals of how i live my life in being loving, accepting and kind, and go from there while trying to muddle through things that puzzle me.