I don’t actually agree with this. A lot of the black and white argument is around dictionary definition of the word ‘woman’.
Language evolves so that the same word can have more than one definition. So ‘woman’ can be ‘adult human female’ and ‘person who identifies as female gender’. As separate definitions.
I agree with you and I don't.
I agree that language means whatever we collectively use it to mean and that can and does change.
I don't agree that the black and white argument is simply a difference of agreement around dictionary definition of the word ‘woman’.
If Woman had always been an identity alone, a way of expressing an inner knowledge about oneself and the group to which one feels kinship in the same way that, for example, "goth" or "Scouser" or "intellectual" is, there would be very little concern if that meaning changed over time. The definition of Goth does not need to be black or white because no formal or social protections or rights exist that are specific to Goths. That doesn't mean there are not Goths, just that it's fine to determine it on the fly in contexts where Goth or Not, or Goth Enough, matter - bouncers at goth nights, goth subreddits and so on - and the definition can be fluid and change between individuals, in different contexts or over time.
The black and white argument is being made in the case of Woman because, IF indeed the language has changed, there are rights, protections and opportunities, whether formal/legal or through the social contract, that pre-exist this change. These pre-existing provisions should not be assumed to apply to changed meaning simply because of what is essentially a coincidence of language, that a word that used to mean adult human of the female sex now also, or instead, means something else.
That is the reason for appeals to authority in the form of the dictionary. The new meaning of the word under which access to these provisions is being demanded is not the same as the meaning of the word under which they were set up.
Forget the word Woman for now. We have group A (the people the word Woman originally meant, and the people for who these provisions were made). We have group B, the people who the word Woman (arguably) now means. There may be some overlap in the groups, but without the word Woman there is no argument to say that the provisions of Group A are rightly also due to Group B.
Without the word Woman there is no case, and that is why the meaning of the word Woman is important and cannot be left to personal choice.
That is not to say there could never be an argument to open them up. There are plenty of examples where a succesful argument has been that the provisions for one group should be open to another, or to all. But those arguments need to be made openly and honestly, and include whether the provisions themselves need to change as well. There is no logical or indeed moral basis whatsoever for one group having a legitimate claim to the provisions of another simply by claiming the same name.
(I have not considered here whether this really is an authentic change in how the population is using these words or an inauthentic one being pushed into the population by pressure groups and threat of social/legal punishments because my argument stands in either case. It doesn't rest on the validity of the change in language itself but on the validity of what is being claimed on top of it)