I have read the article you linked signed by scientists from a wide spectrum of disciplines.
It was a reaction to to some US domestic legislation that was being proposed and as such refers repeatedly to the draft legislation. There is no link to the draft legislation. I am not familiar with how the US drafts, enacts and uses domestic legislation. I believe it is quite different to the UK system. I do not believe the US has equality laws as robust as in the UK and the EU.
So I cannot really comment on the argument, except as inferred from the reaction document linked.
The proposed policy seeks to erase the identities of millions of Americans who identify as transgender (individuals whose gender identification differs from their assigned sex at birth) or have intersex bodies (individuals with biologically atypical patterns of male and female traits).
I do not believe that the UK has any plans to make it illegal to identify as transgender. In fact, the UK includes the characteristic of gender reassignment in the equality act. I would argue that there is very little chance that the UK will attempt to enact legislation banning people from stating that their gender identity does not match their sex.
I am unfamiliar with US legislation affecting people with disorders of sexual development, described using the word "intersex" in the text.
Given what I do know about the US healthcare system, I am unsurprised that people with congenitial disorders like DSD face challenges in accessing proper care. Given what I know of the US legal system I am also unsurprised that people with DSD in the US have difficulties if their biological sex is not correctly identified by the time the baby's birth is registered. Fortunately we have the NHS in the UK, which I am told is pretty good for people with DSD. I have not heard of any complaints about their legal identity from people in the UK with DSD.
I am not clear on the relevance of this letter to the topic under discussion.
I agree with the signatories that it would be unconscionable to use the pretext of science to enact policies that overrule the lived experience of people’s own gender identities
Like with religion, if a person chooses to believe in gender identity they should be free to do so. Any perceived mismatch between a person's gender identity and their sex should not matter so long as law is well-drafted to make clear which laws are is sex-based and which are not.
Again, I do not see the relevance of confusion in the US between gender identity and sex.