If you're going to do a binary, X and Y chromosome doesn't hold up due to the presence of functional XX males from an SRY gene. Its speculated most Y chromosomes started as X chromosomes in animals that have that dichotomy.

In fact a functional or non functional SRY gene is a better determinant for biological sex.

The fact is though that testerone and SRY receptors have relatively high variability and trying to socially stress people into a group of traits will create a feedback loop that is opposed to more natural courses of evolution.

Its likely trans people - of whom there are records of going back to time immemorial - are likely an evolutionary adaptation and serve some evolutionary function to society we may not yet understand

Since gender is socially constructed (male norms, female norms, male jobs, female jobs) the presence of trans people in society that not only understand both sets of roles but can navigate them is probably an advantage over societies where those roles are less fluid and more strict.

There's a case to be made that the more strict gender roles become, the more evolutionary pressure there is to create trans people.