No @Tandora, we do not need to fix the very basics which is that people simply don't understand what being trans is. before we can start having reasonable conversations about policy,
All we need to know is that whatever it is that makes a physically male person "trans", it is manifestly a different thing to being identified as having the type of human body that is easily recognised as female at birth, and therefore a person being recognised at birth as male bodied but later unerstanding themself to be "trans" , whatever that is, does not give the latter any moral claim whatsoever to being interchangeable with the former in all, or indeed any, scenarios where sex matters.
"Women's" spaces, "Woman's" rights, even the language of "woman", "girl", "female", "she" - these things did not pop out of the ether fully formed. They were responses to the observable existence of female bodied people. That is the originating fact, a real world pragmatic response to what was observed on the ground.
The putative existence of a much more complicated different group of people as yet to be defined is totally irrelevent.
Just as a jelly is shaped by its actual mould so the theoretical existence of moulds that have a different shape is not relevant, so Women's rights, supports and protections were shaped by the actual needs of people. These people were historically known as "women" simply because that was the name for their type of body. So the theoretical existence of other ways to define the word "women" are not relevant to those provisions because it was the facts of the people drove the provisions, not the other way round.
That there may be another way of thinking about "sex" such that you can draw a different line that includes most, but not all, of the female-bodied people, and few, but not none, of the male bodied people, does not mean the group of female bodied people ceases to exist, nor does it mean the social and historical expereinces of being female-bodied somehow never happened.
And that means it is also not a justification to remove the rights, resources and language of the female-bodied people. It just means you changed what the word "sex" means. The people and their needs still exist in exactly the same way
So you can have your "multidimensional variable with various components" as a truth in the world, certainly. What you can't do is use that to undo the fact that having the type of body that is boringly and everyday recognised as female still has real world consequences and that in itself is enough to make being female meaningful and separate and in the final analysis nothing whatsoever to being a "trans woman".
Simply put, whatever that latter might ultimately prove to be, what they are undeniably not is female bodied. And that is all we need to know to have these "reasonable conversations about policy" with respect to the rights and needs of the half of humanity who are female bodied by those boring everyday physical measures that humanity has used for millenia.
So if you want to change the "policies" that are based on the needs of the simply boringly everyday physically female, those "conversations" need to start by explaining exactly why the belief that some male people have minds aligned to female bodies while actually having male bodies should be used to leverage changes to policies that exist to protect the interests of people with female bodies.
It is not for female people to justify why we should exclude trans women. That is obvious - they are not female in the boring everyday physical way for which these resources exist in the first place.
It is for the people who want to open up female language, history, protections and rights, things that are undeniably meaningfully attached and specific to the female of the species, to certain male people based on nothing more than some theorised-but-as-yet-to-be-even-proved belief in an undiscovered commonality of mind that links most, but not all, female people, and few, but not none, male people that you want to name "sex" or "gender", to justify exactly why that un-prooved quality, should it even exist, is more relevant to the purposes of single sex language and provisions that the simply observable fact of sex by which they came to exist in the first place.
(And don't tell me "the fact trans women report how they feel is the proof" unless you are also prepared to accept genuinely felt personal testimony is also proof of the objective existence of ghosts, the Blessed Virgin Mary and aliens)
The burden of proof here is not on the people saying "whatever is in his mind, is it not interchangeable with the physical fact of being female bodied in this world" , it is with the people who believe something in a man's mind makes him interchangable with female-bodied people in a way that no other man is.
That is the reasonable conversation about policy. And that is the one you are unable to have.