Okay, so given the replies so far, I will make a bit of a longer argument:
I will argue that assessments that people are or are not women or men made by people like feminists usually insulted as 'TERF', or conservatives (or by the vast majority of the population, but I do not need that) are generally
true, even if we assume for the sake of the argugments that similarly-looking claims made in a new variant of English are true as well. Terminology: I will call the assumed new variant 'W-English', and the other one 'T-English' (for "Woke" and "NW" respectively), but please pick your choice of terminology, as this is not relevant to my arguments.
So, first imagine there is a word in language Z speaking by a population, which is 'tutu', and means 'horse', in 1990. As time goes by, some speakers of Z change the way they use the word 'tutu', and now they mean 'car'. But some others do not change the way the speak. Some new community members adopt the new usage as well. But some others do not. By 2021, about 50% of the population uses 'tutu' to mean 'car', and the other 50% uses 'tutu' to mean 'horse'.
Suppose a person in the second group sees a horse, and she says that that's a 'tutu'. Surely, she did not say anything false, or mistaken. The meaning of the words is given by usage, but if there are two sizable chunks of the population using 'tutu' to mean very different things, that does not mean those using the word in one of the senses are making
false statements, in the language Z. How big the chunks need to be it's a debatable matter, but I would for now say that if one usage has, say, 20% of the population, that's enough to make it a common usage, not a case of making false statements as a result of a mistake about the meaning of a word. Further,
if the two groups fail to understand each other, then Z split into two dialects Z1 and Z2, and speakers of each are unaware about the meaning of the words in the other dialect.
Now back to English: there is no good reason to think that the people older than, say, 40, who say that a person who would say that transmen are not men or that transwomen are not women ever changed what
they mean by 'man' or 'woman' from 1990 to 2021. In fact, there are very good reasons to think they have not changed the way they use those words: these words allow them to talk about the properties they care about just fine, whereas the proposed new terms do not (even assuming the latter are coherent). So, why would they change the way they speak? Some might say whatever the Woke wants them to say when coerced, but that does not suggest a change in usage when not coerced (or even when coerced, as they will likely see themselves as making false statements in NW-English, rather than true ones in W-English). And clearly those resisting are not giving up to the coercion. And similarly, many younger people also say the same things, and there is no good reason they're speaking W-English, rather than NW-English - which coincides with 1990 English on the meaning of 'man', 'woman', etc. On the contrary, the evidence shows they're not speaking in W-English, as their assessments of who is a man or a woman regularly match NW-English, and further they deny claims that would be trivially true in W-English (again, assuming for the sake of the argument the coherence of the latter).
That leads me to the following point: the statements above or similar ones are
true - whether they are true has to be assessed in the language in which they are spoken, not in some other language or dialect.
The above has implications for accusations of 'misgendering', which are generally
false. To see this, let us look at some dictionary definitions:
to identify the gender of (a person, such as a nonbinary or transgender person) incorrectly (as by using an incorrect label or pronoun)… See the full definition
www.merriam-webster.com
to identify the gender of (a person, such as a transsexual or transgender person) incorrectly (as by using an incorrect label or pronoun)
So, to misgender a person involves an
incorrect identification. But that would involve making
false statements, rather than true statements in 2021 NW-English. Here's another definition:
en.wiktionary.org
(transitive) To refer to (a person) using terms that express the wrong gender, either unknowingly or intentionally; for example, calling a woman "son" or a boy "she".
And again, no misgendering involved in
true statements, which do not express the wrong gender because, whatever 'gender' means, the statements are
true, so either they express the correct gender, or they do not express any gender whatsoever.
The world's leading online dictionary: English definitions, synonyms, word origins, example sentences, word games, and more. A trusted authority for 25+ years!
www.dictionary.com
to refer to or address (a person, especially one who is transgender) with a pronoun, noun, or adjective that inaccurately represents the person's gender or gender identity: At first my teacher misgendered me.
That was seems harder to understand, as it involves 'gender identity' and pronouns. But still, this requires
inaccurately representing a person's gender or gender identity, which true statements do not do.
Another one:
Definition of misgender verb in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
www.oxfordlearnersdictionaries.com
misgender somebody (as something) to refer to somebody in a way that does not represent the gender that they identify as
If we take that literally, to refer to someone as 'American' would be an instance of misgendering, since such labels do not represent any gender - whatever 'gender' means, it seems to me it's not that one!
But then, maybe the dictionary above means it's to refer to someone's gender in a way that contradicts with the gender they identify as?
If so, then a true statement of the form 'A is a woman' or 'A is a man' can only be an instance of misgendering A if A's gender self-identification is
false. Why? Because true statements do not contradict true ones. What? Self-identification cannot be false? Okay, then a true statement of the form 'A is a woman' or 'A is a man', or a true statement in NW-English stating 'transmen are not men', etc., or any other true statement, can never be an instance of misgendering.
But I'm sure one can find more definitions, so pick your choice. I would still argue that it is improper to assess the accuracy of statements made in NW-English by the meaning of the words in W-English - even assuming there is a coherent meaning in the latter -, and that there is a sizable chunk of the population (I'd say the vast majority at least, but I do not need that hypothesis here) that uses the words 'man' and 'woman' to mean what they meant in, say, 1990, or for that matter 1970 (even if minuscule proportions of the population might have already used them differently in 1990 or even 1970).
What about pronouns?
Speakers of NW-English are using the correct pronouns in their language, namely NW-English. And they are using the correct pronoun. Maybe not the pronoun some people want to be called by, but the pronoun that matches the words that they are using in the language they are speaking.
Now, why would they want to speak in NW-English, and not replace it W-English? Are they evil people who want to harm trans people?
Save for weird cases (which might exists on either side), not remotely. What they want is to keep talking about the stuff they care about, in this case the properties of being a NW-woman or a NW-man. But that's another matter: the fact remains that people talking in NW-English are generally not making false claims in the situations as above, and not misgendering anyone, at least in any of the definitions of 'misgendering' above (if there is another definition that you think matches usage and you would like to discuss, please let me know).