The one comment is so so eloquent. Will be lifting some of it to write to my MP. Absolutely nails it. 
You make a lot of good points about how society treats men and women differently, then make the leap to saying that men should be able to self define as women without consideration of three crucial points:
We’re not yet in a society where men and women are treated equally. Men who ID as women are not treated by society as women, they are still afforded privilege in many areas. They are being afforded privilege right now, for being allowed to trample over the legitimate concerns of women, to validate their feelings and demanding that they want to be treated as women. That no impact assessment on the effect on women and girls is happening, and that the message that women don’t even need to be consulted about the change of the very definition of the word woman, shows how little society regards women, still.
We’re not yet in a society where men and women behave in the same way, nor one where gendered patterns of violence don’t exist.
Men for example demonstrate behaviour based on experience of male privilege. Men also have male patterns of violence which are VERY different from the offending profile of women, as a group.
98% of sex crimes are committed by men in the UK, for example. And 1 in 5 women have been the victims of sex assault since they were 16. (The figure rises if you include assaults that happened when they were children.
The question is “does transition / IDing as the opposite sex change the offending behaviour of people with male bodies to match female crime levels?” and the evidence seems to be - no it doesn’t. Looking at UK prison stats as an example, 60 transwomen are there for sex crimes (this is possibly nearly 50% of them). This compares to only 3% of women (120), and 19% in the general prison population.
You’re completely ignoring the impact on other people, especially the rights of woman and children to draw their own boundaries.
You say:
“If we wanted to divide people into those who can perform care work well and those who cannot, then no aspect of gender/sex would help us do this, because the skills necessary for care work don’t have anything to do with gender/sex.”
And this goes to the crux of the problem. Nowhere in this statement did you consider the feelings, dignity, autonomy or safety of the person receiving the care.
Women have a right to be able to demand female carers. Particularly where we are vulnerable or in a state of undress. An elderly woman in a care home, for example, should be able to ask for a female carer, and not expect a “woman” with a penis to be helping her get dressed, or doing intimate care like washing her genitals.
A women asking for a smear test should be able to request a female carer and not have to have a “women” with a penis appear. Widening out beyond care, women traumatised by rape should be able to expect to not have to share a bedroom with a stranger with a penis in a hostel, refuge or crisis centre. Women should not have to share cells with criminals with pensis. Women and children should not have to come across penises in changing rooms or in hospital wards.
We should be able to have our dignity and boundaries respected.
Also - it is people with penises who harass, sexually abuse, sexually intimidate and rape women, as well as low level stuff like voyeurism and persistent, inappropriate sexual comments. If you call some of these people “women” and demand women allow them into our spaces, women and children will suffer. Transactivists like to counter this with “you’re saying all transwomen are predators, you’re a transphobe!”. But no, this is simply saying “transwomen show male pattern violence”. Nothing special, not all of them - but as a group, much more like men that woman as far as crime is concerned,
I agree with the points in your article that we need to distinguish between gender and sex and be clear we mean when we are talking about gender. We shouldn’t shy away from using the word sex when this is what we mean.
It seems to me that most of the modern wave of transwomen (that is, those who are transgender, not transsexuals with dysphoria) are identifying with femininity, not actual womanhood. They are identifying with an idea of what it means to be a “woman” gained from society, media, advertising and porn. We need a new word for this in my opinion. Not the word woman - it has a meaning already. It means adult human female. This does not include any person with a penis.