This question came to me kind of on the back of thinking about the Seahorse documentary and related legal battle that Freddie is undertaking to be named as the father of the child they birthed, rather than the mother:
When someone gets a GRC they get a new birth certificate, right? Is it in any way distinguishable from a standard birth certificate, in the way that adoption certificates are (where adoptive parents are listed as mother and father, but the certificate itself is a 'Certificate of Adoption' rather than a 'Certificate of Birth').
If it is marked in some way as different, then does this become the only route for a child like Freddie's to discover who birthed them (i.e. that their father is actually their mother)?
There's other inconsistencies here, as others have previously pointed out, where children are donor conceived. Donor is not listed and not indicated by any kind of differentiation in the certificate so although parents are encouraged to tell children they are donor conceived and donors can be traced after the child reaches 18, if parents decide to withhold that information, the child may never find out.
Sorry, not sure that was a coherent question, but it's an interesting area.