I mean socially, if people respond to trans women as women, then that's a huge aspect of being a woman. 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. I'm sure you wouldn't go on HRT with hormones of the opposite sex, as this would change things about you in strikingly dysphoric ways for you.
Some trans women are cis-passing, especially those that transitioned early, and people won't even realise they're speaking to a trans woman. Others who transition later in life may not be cis-passing, and people will tell pretty quickly that you're trans. But 99% of people in my experience treat trans women with courtesy and respect according to the gender they're presenting, and let them live their lives, understanding the upheaval they've gone through, and if they're literally not posing any harm, then to let them be.
If trans women were men, then they wouldn't have transitioned into another type of being/existing. The deep discomfort with being a man forced them into a transition that allows them to live their lives within a society that seems generally able to accommodate that, and which fits that trans person much better than the way they were before. It's not just about clothing (you say 'I'm all for people presenting, dressing as they please' - I agree), it's about bodily changes and social changes, it's a cluster of significant changes that make you become something different to before, socially and biologically.