I've been swimming and reflecting on the new purpose of the word "women".
The usual purpose of words is to describe something that exists. For anything that exists in nature or comes into existence organically, the thing exists before there is a word for it. The more fundamental the thing is to our understanding of the world, the older these words are in human language, e.g. woman, man, mother, father, eat, sleep. But new words can be invented to describe things which have been in existence for a long time, for example, a botanist discovering a previously unknown plant species and giving it a name, or someone in human history realising that there was no word for two legged animals and coming up with "bipod". Sometimes the word for the thing comes into being contemporaneously with the thing itself, such as when you invent a new drug and come up with a name for it. Occasionally the thing cannot exist until it has a new and unique name, for example, a Twitter profile.
What is extraordinary about this new version of the word "women" is that the word for the thing existed before the thing itself, and indeed the thing can only exist because the word already existed.
Category words describe groups of things or people with at least one common feature not shared by things or people outside the category. The only common feature shared by all the people in my updated definition of "women" is that they are using the same word to describe themselves.
You could create a category of people consisting of adult human females except those with a male or non binary gender identity plus adult human males with a female gender identity if you wanted to and call it "aeronautical noodle monsters" but they would not have anything in common and nobody else would use this term. If the only thing they have in common is using the same word to describe themselves, the only way to make them use the same word to describe themselves is for male people with a female gender identity to take the word that almost all female people have been using to describe themselves for over a thousand years and start using it to describe themselves. It is by male people appropriating the word women that the new category (essentially, "people who refer to themselves as women") comes into existence. And once it is in existence, you then begin arguing that it is this group ("people who refer to themselves as women") who need their own toilets, prisons and sporting categories, and not "adult human females". This is now easy because toilets, prisons and sporting categories are already labelled as being for "women" and "men", and even if the adult human females wanted to change this to restore the status quo ante, they no longer have a word for themselves so what would we call it?
That's why I have grudgingly come to the conclusion that I do not agree that people should be allowed to identify as whatever they like. Because you cannot identify as a woman without appropriating womanhood and and co-opting women into your identity without their consent.