This is a parents rights case. It feels a bit like those cases where parents and doctors have disagreed in court about the child’s best interests. You often find in the background of the disagreement a religious or political feeling on the part of the parents which they are pursuing in respect of their child. Also there is often some kind of trusted highly influential adviser to the parents telling them what they should do, who doesn’t have the knowledge of that individual child or who doesn’t turn out to know much about children or medicine at all. 
I hope the parent in this case has good, objective, trustworthy support for themselves and their child.
There are older threads on FWR about this legal case:
www.mumsnet.com/Talk/womens_rights/3370188-transman-gives-birth-wants-to-be-father-parent
www.mumsnet.com/Talk/womens_rights/3271483-Baby-could-become-first-person-born-in-England-or-Wales-without-a-legal-mother
I do think the problem here is the GRC.
It is a legal document saying that gender is a real thing that overrides biological sex, but in certain circumstances only. It doesn’t seem clear about what these circumstances are, making friction with other areas of the law which are clearly written for biological sex. But in reality everyone knows that biological sex can’t be overridden. Which is why a sperm donor, not an egg donor was needed in this particular case. Because no human being can actually change sex.
It is legitimate that other people than the individuals concerned have an interest in what goes on birth certificates.
I guess that’s why people who get a GRC aren't allowed to change their sex on their original birth certificate. The GRC gives them a new alternative BC with new legal sex written on it, but the old one still exists in the archives.
And that must also be why we don’t let parents just put whatever sex they wish for the baby, on the baby’s birth certificate.