But given that we live in a society where a man dressing as a woman, calling themselves a female name etc will be the target of abuse, a certificate saying that this is a permanant arrangement, person has had a meaningful transition etc, is a way of formally recognising their status whilst retaining the reality of their sex.
I understand what you're saying. But you need to unpack it.
Firstly, how would you ever police what clothes constituted the required status?
Secondly, it would mean that no one else could wear those clothes without begging the question are they trans? Thereby cementing all the gender boxes again.
Thirdly, many men use dressing in what they consider to be female clothing, as a sexual fetish. Why should they be given 'a status'?
Within the bounds of what is considered appropriate, no one should be discriminated against, based on what they wear. It's clothing.
And lastly. The clothing is irrelevant. It's to signify that they want to be treated as the opposite sex, or excluded from the treatment that they consider normal for their sex.
The notion that we treat men and women completely differently, all the time, is based on sexism.
Let's address the reasons why people think they get treated differently if they present as the opposite sex. Rather than saying of course you must pretend to be the opposite sex, if you want to be treated a certain way.