This is all taking the statement out of it's context, which is medicalized and only relevant in a situation where the person in question is not, in fact, a woman.
I'm about as critical of gender ideology as you can be, and I think it does tend to lead to sexism because of the larger implications, but it is not really useful to treat this statement in a way that completely decontextualizes it.
I hear you LobsterNapkin, so how about we set some parameters towards defining that phrase ourselves.
So, as you rightly point out, the phrase "living in the acquired gender" originally referred to individuals who had medically transitioned and who were now seeking to legally change sex.
Going back to the discussion and public information disseminated by the UK Government during the time of passing the Gender Recognition Act Bill through parliament, this was very much aimed at putting the public in mind of the feminine male homosexual transsexuals or masculine female homosexual transsexuals who would transition medically as far as both their own health and the available healthcare at the time allowed. For males this almost always involved genital surgery. For females, because genital surgery is even today riskier with high rates of complications, this wasn't the case. But because testosterone is a hell of a drug, they often successfully passed anyway.
So the phrase as originally intended applied only to individuals who had removed secondary and primary characteristics of their birth sex (as much as possible), whose bodies had further changed through cross-sex hormones and possibly a range of cosmetic procedures. They passed as the opposite sex for all intents and purposes and would largely be treated by society as if they were members of the opposite sex.
The phrase "living in their acquired gender" is using gender here as a synonym for sex.
Can we agree that the phrase only makes sense in this specific context?
And if you agree with that, then would you also agree that the phrase "living in their acquired gender" has no place in laws, policies or regulations based on gender identity (or self-id)?
It's not asking you to say that only women can be nurses, or they can't wear hoodies. But I don't really believe that anyone doesn't recognize that William is usually a male name and Sue a female name, or that we have pronouns associated with our sex, or that there are some clothing and fashions that are more associated with one sex than the others. That's not what a stereotype is. And I would maintain that these female associations are not somehow "lesser" than the male ones.
I wonder if you're parsing "stereotype" in its secondary meaning here, and not the primary?
The primary meaning derived from its etymology is a "firm impression". We have firm impressions about what attributes certain groups of people have in common. We get these impressions from observing people and using the pattern recognition skills we develop in early childhood.
These stereotypes can be accurate or inaccurate, they can generalise and oversimplify, depending on what the stereotypes are. Although it is often believed that stereotypes are always negative beliefs about groups of people, this is not true.
As you point out, if we sorted people by their first names, if you then looked at a group of Sues and a group of Williams, almost all of us would expect to see a group of females and a group of males respectively. That's an accurate stereotype. (It remains accurate even if it isn't always true. Because stereotypes are beliefs we have about groups of people, not all members have to share all the attributes that make up the content of the stereotype.)
The secondary meaning, which we are mostly concerned with here is that of stereotypes about men and women, classed into binary hierarchies, of which the ones associated with the female sex are inferior to the ones associated with the male sex. Even if all of us did indeed share the attributes in question (such as being caring, emotional, good at cooking etc), that hierarchy is already a problem, because it decrees that we are inferior if we have those attributes.
That problem is then compounded by the society we live in, which seeks to impose these stereotypes on us and punishes non-compliance. Given that the attributes associated with the female sex are considered to make us inferior creatures when compared to men, it means that we cannot win. Comply and submit to the hierarchy or refuse to comply and be penalised.
We are in agreement that the stereotypes associated with the female sex are not inferior. I hope we are also in agreement that they shouldn't be imposed on us in any way?
If a person who is male is using titles or language usually associated with women, and taking on other cultural customs associated with women, there is a sense in which they are doing something different than what is usual, and in a deliberate way. Saying that none of those things makes someone a woman doesn't make that less true.
Well, it's true that a man who calls himself Sue, wears dresses and loves cake decorating etc is deliberately "doing something different". But why should that be meaningful in laws, policies and regulations? (And let's be frank here, he is not merely doing something different, he is giving up power and deliberately adopting attributes considered inferior.)
So taking these stereotypes you listed above, our phrase "living in their acquired gender" is now referring to a different concept using gender as socially constructed stereotypes (or what I call sex stereotypes and sex role stereotypes).
And governments are now using the phrase in this latter meaning, where living in your acquired gender means adopting the sex stereotypes and sex role stereotypes associated with the opposite sex.
It's no longer connected to post-op transsexuals treated as the sex they wish to be, but to physiologically intact males and females following their preferences for feminine or masculine stereotypes respectively.
What this means is that governments who are seeking to enshrine gender identity in law are seeking to enshrine sex stereotypes and sex role stereotypes in law. And that phrase "living in their acquired gender" is hugely damaging to women because of the hierarchy.