I am not sure I have followed all the arguements on this thread and some of the issues I am not informed enough about.
However, the initial response to the article and court case is about the simple biological fact that a female person who actually gave birth to a child is the biological mother.
To try and argue that you can be registered as the "father" is as non-sensical as saying we are "assigned" our gender (euphamism for sex) at birth.
Birth certificates have all sorts of signifigance but particularly for the child itself. And any bending of the truth is not in their interests.
Also, though a bit off topic, many children who are fostered out and / or adopted out of their birth family often only find their true story through their birth certificate. And in some cases are also important in terms of inherited health issues.
This is a futher example of the unintended consequences of the fairy story of the GRA.
I think birth certificates should not be allowed to have the "sex" of the child changed, and have the birth mother recorded.
And it is these facts that should be used when recording crimes, health statistics, housing, income levels, etc.. (Not forgetting the "man" who turned up at A&E with stomach pains which nobody could explain until the "man" give birth. Hospitals shouldn't be put in this sort of make believe.)
If it means we now need to have additional paper work for "identity" issues, so that those who want to imposed their internal vision on others let that happen.