"I mean socially, if people respond to trans women as women, then that's a huge aspect of being a woman."
No, it is not a huge aspect of being a 'woman'. The logic doesn't support this argument at all.
"People don't have the capacity to see chromosomes or whether a person has a uterus, they judge people on appearances and a cluster of significations like secondary sex characteristics. If you've medically transitioned as a trans woman (including HRT, surgery), then you'll share these characteristics with other women (including biological characteristics like hormones and sex characteristics like breasts, vulva, softness of skin, body hair growth), and this is what society will see, and will treat you accordingly. You talk about scientific criteria, but these are significant scientific/biological changes."
Firstly, less than 5% of the male people who identify as being transgender have any type of surgery. And in that 5% is facial surgery so it is much less than 5% who have a cavity inserted into their groin. So, when it comes to 'treating a transwoman as a woman based on appearance' your bringing surgery into the discussion is completely irrelevant to your other points.
It also is irrelevant as to whether that person is a 'woman'. Because they are not. They remain as male as they always were.
Maybe you can answer the question:
What is the difference between a male person who has had their penis and testicles removed because of injury and disease and one who has had extreme body modification to fit their own personal philosophical belief about themselves?
Why is one to be accepted into female single sex spaces and the other not?
"then you'll share these characteristics with other women (including biological characteristics like hormones and sex characteristics like breasts, vulva, softness of skin, body hair growth), and this is what society will see, and will treat you accordingly."
Soft skin... Fuck - that leaves me out of the category of woman! When you repeat this statement, do you see the falsity there? There are people out there who have other extreme body modifications, reptiles, vampires etc. Do those body modifications also then move those people into the category of the thing they are are emulating with their extreme body modification? Or ... are they just their original category based on the coding of every cell in their body - human?
Your fallacious argument fails if someone rejects the pseudoscience and false logic needed to support it. Just because a male person has grown breasts, has a fake vulva, doesn't mean that other people cannot correctly identify the sex of that person. Because the brain processes the complete person that someone is analysing. From voice to pelvic alignment and q angle (and no, no one needs to see anyone naked to assess the posture of others) .
It sounds like you are simply repeating falsehoods from activists now.