Does it list gender, or sex?
Btw, I don't know about birth certificates over there, but if it's 'male' and 'female', genitalia are a generally reliable though imperfect means of determining it.
Relevant questions are: What does the claim in birth certificates mean? What are birth certificates saying? Are they using the words "female" and "male" in the usual sense of the words, in English?
Good question. Here in the UK, apparently:
"Birth Certificate: All babies are assigned a gender on their birth certificate. Usually this is in line with the sex of their genitals, though in the instance of intersex children, doctors usually determine which sex should be assigned."
And later on the same page:
The Gender Recognition Act 2004 created a process to enable transgender people to get their UK birth certificates and legal gender changed.......... The Birth Certificate drawn in this manner is indistinguishable from any other birth certificate, and will indicate the new legal sex and name.
http://www.thefocustrust.com/info/legal-documents/birth-certificate/
Is that slightly confusing or is it just me? The page is by an organisation that in its own words
"exists to provide social, educational and recreational activities for Transgender and Intersex individuals", so one would think they would be clear about it in their own minds.
I'm not surprised they are not clear, as usual claims made in thise sort of context are at best unclear. There is also the issue of the meaning of "gender" in British vs. American English. At least until recently, in my experience (not much, though), 'gender' was used in the UK in contexts in which 'sex' would have been used in the US.
But in any case, most people in the UK were born before 2004, so the meaning of the claims was not based on the Act they mention. Unless there was - very unlikely - a definition of 'sex' in the UK in the past, the meaning of the words was that in colloquial usage, or else in medical usage if there was any difference between them. I take it that the colloquial meaning in question is not about gametes, but that the sex of an individual (human or not) depends on the gametes they would, under some normal circumstances, produce (analogy: the meaning of 'water' is not about H2O, but whether a liquid (to make it simpler) is water depends on whether it is composed of H2O, at least primarily).