This.
If you redefine the word "woman" to mean someone with a particular gender identity rather than someone of the female sex, that new definition excludes most actual women.
Now yes, some words have multiple definitions. A sole can mean a type of fish or the bottom of your shoe. But we never refer to those things together. You wouldn't, for example, find fish in a shoe factory or use shoe leather in cooking. When you use the word "sole", it is going to be obvious what you mean from the context, and nobody is going to need to clarify whether you mean the fish or the bottom of a shoe. They might use the same word but there is no category of things consisting of, alternatively, a type of fish or the bottom of a shoe.
So why on earth do we need toilets, prisons and sporting categories for female people or, alternatively, male people with a gender identity? What is the point of this category? These are two things with no common features.
But because when we are talking about people, and who has the right to be in which space, there is potential for confusion, and people are going to need to say, "Do you mean female people or male people with a gender identity?", using the same word for both isn't workable.
And the reason they insist on using the same word for both is precisely to create confusion, to pretend that a male person with a gender identity is the same as a female person, and to force team female people with male people with gender identities against their will.