You're pretty clear here and elsewhere that your "trans-inclusive" definition stands - it's "objective" and ours is "subjective". You're also consistently clear that this is the basis on which you understand yourself to be a woman - you're seen as one by everyone else. Woman is, to paraphrase you elsewhere, socially/culturally constructed.
My use of 'objective' and 'subjective' above was in reference to my life as a woman, discussed on this website. It wasn't meant to be a 'trans-inclusive' definition.
I base my understanding about myself on my experiences, my socialisation, the way I am limited, the obstacles I've had to overcome, the way I am included. This is amongst knowing how I feel about my experiences and how my feelings and my experiences are shared with friends, relatives, colleagues—everyone I share a relationship with. This is consistent across every culture I've been in, in many countries. My experience and existence doesn't change at borders. That would be really weird.
Your "objective" feels like a weak point in the argument. Acknowledging fallibility - anticipating counter-arguments - often strengthens an argument (proverbs about willows bending in the wind or whatever). Certainty in the context of a claim about a word's meaning globally and throughout human history (and which has just been clarified in UK law and is the subject of heated national debate) does make the claim look a bit suspect.
I stated on the first page of this thread, I believe 'woman' can include trans women, but is not all-encompassing. I believe there is a very large social aspect to this, but it isn't just showing up. It isn't 'passing' or the clothing destination, which these discussions always return.
I don't believe my beliefs should be enforced any more than any others. I don't even think I can represent any specific boundaries around it, because I don't think about it. It might be a visceral reaction? It may be a rationalisation? It would definitely be case-by-case rather than a rule. It's definitely not a measurable quantity of 'something.'
I've also said that I believe defining sex by biology cannot work because 'woman' and 'man' have very social and cultural meanings that may not be the first definition, are understood to be relationship-based, social-role based, and identify-based. Denying the other uses serves to shut down discussion. For example, I've met more than a few trans men who told me how they struggled with men actually treating them like men. I'm assuming men aren't thinking about gametes here.
Do you really believe that, in a majority of countries and contexts now, and throughout human history, a woman dressed as a man and subsequently discovered to be female would be met with the reassuring cry of, "Oh, yes, he's definitely a man - he's wearing trousers, after all!" Take what example you will - the apocryphal Pope Joan, the girls who've disguised themselves as boys in wartime to protect themselves from rape only to be "uncovered"...
No.
Are you honestly saying that, for the entirety of human history and, indeed, across the world now, the discovery of what was beneath their clothes would be met with an immediate and ringing endorsement of their initial outward appearance and behaviour - of the first impression they created before the truth was revealed? "Oops, sorry, my lad. Off you go now!" or "What a man that pope was!"
No.
How does your (emphatically objective) definition hold up in this thought experiment, based on everything we know of human history?
Again, I wasn't using 'objective' and 'subjective' this way, but let's go with this...
Until modern medicine, the biology of sex was only 100% accurate when babies were born. Everything else was an assumption based on the beliefs and assumptions of who a woman or man looked like.
Today, cultures socially group men and women separately. This is largely biology-based, but not completely aligned with gender critical genetic beliefs.
So yes, there is some 'objective' and some 'subjective' in there, according to gender critical uses of sex-based definitions across human history to today.