Also, the gender of a trans woman is feminine, not female.
Sex= female or male
Gender = masculine or feminine.
To pick up your argument cistern , yes, you could say a transgender woman has taken on attributes which society deems feminine. But this does not make them female.
If a woman wears ‘boyish’ clothes, then she could be seen as dressing in a masculine way. But what are ‘boyish’ clothes? They are the clothes society deems acceptable for men to wear.
The whole reason the language around trans has changed from transsexual to transgender is because human beings can not change sex (other than legally following surgery). Gender is what society deems masculine or feminine, hence can be changed.
So what I think you mean cistern is that women have ‘cis-privilege’ because they are female-bodied, they can wear what they like and still be recognised as female. Whereas trans women have to perform society’s idea of what being a woman is.
I get that, for trans women, performing what you are not is exhausting. But is it not then easier to work on self-acceptance? And if masculinity does not sit easily, challenge the constraints of that, not appropriate womanhood?
The ‘privilege’ of being able to wear masculine clothing (trouser suits, legal dress etc) is, for women, the result of hard won fights to access public roles, employment, partake in sporting activities, and civil and public life. Space which was, for generations, reserved for men. Tailored suits, whether trousers or skirts, high vis vests and work gear, all of these things give women access to previously male domains and earning capacity.
What are transgender women seeking access to by wearing feminine attire? What ‘privilege’ is with held? It’s not the right to education, or employment, or civic and public life. These are already in their grasp. It is access to female same sex spaces.
Female same sex spaces exist because being female, regardless of how one dresses, is a risk, not a privilege.