As someone who happens to be a trans woman, I'm trying to work out if commenting here is basically just stupidity, in all likelihood it probably is. But at least as they say nothing ventured nothing gained or lost.
The current legal version of a woman/female is someone who is assigned it at birth or someone who has become one through the process of applying for and being granted a GRC.
With the exception of sports and marriage by a religious figure there was a time between the GRA passing and the equality act passing where trans women granted a GRC couldn't be excluded from single sex spaces. This is slightly more ambiguous now with the equality act, but exceptions has to be shown to be the least discriminatory method used, and there needing to be a clearly legitimate aim, that can't be achieved by other methods.
I think the issue with a lot of the debate that goes on at the moment is that it often tends to ignore the lived reality of the situation that's happening at the moment, most facilities/services are already inclusive of trans people, and I don't know how many people use birth certificates to access spaces rather than other forms of government ID such as such as passports and driving licenses which are a much lower bar to being able to change.
Separately with regards to the what is an essence of woman I have not a clue, I likely can't explain what makes a woman anymore than another woman can. All I can say is that being seen as, and treated as a woman in every way I possibly can be feels to be correct for me. I know that sounds a bit nebulous but I could probably write a thousand lines and it still would.
I'd also like to say that during transitioning biology changes, more than quite a few people would expect. You sweat differently, skin changes, smell changes, how hair and fingernails grow changes as you absorb and process different amnio acids slightly differently, fat and soft tissues redistribute, muscle systems, and arterial systems change.
Some things remain fixed but lots do not. I have grown breasts that are no different biologically to any other womans when for a period I was hormonally imbalanced I even lactated breast milk, as those structures exist in from birth in everyone to different developmental degrees.
Someone also brought up earlier the downsides of being a woman and I accept that there is clear sexism that exists in society and the work place, do I however wish it wasn't there yes. But would I say I experience this sexism differently from other women my guess would be in many cases no.
I think a lot of people think trans women experience it differently and I think there is some truth to that depending on trans woman but it very much comes down to the individual and their circumstances.
One of the reasons that I have this view is that since tranitioning I also happen to be a survivor of rape. It was quite patently obvious from the fact the demeanour of the man that decided to rape me changed to being disgusted half way through the act, after it became clear that I was trans, that the initial experience wasn't different because I am trans.
And I do think based on this experience it feels disingenuous when people seem to think that being trans you can't experience normal sexism. It was one thing when he was strangling me and forcing me to my knees before forcing me to perform oral sex on them while continuing to hold their hand round my throat choking me, and then something very different when he then wanted more, forced himself on top of me and realised what I was.
There was a clear devide in the behaviour when that man knew I was trans and when he didn't, and so for me for some to claim that there isn't feels as I before stated disingenuous.