yes it would affect everyone. Birth certificates would be nonsense if transpeople could just falsify not only their own birth certificates (as they can now) but other people too. Children have human rights of their own - transparents can't unilaterally remove other people's human rights, though some extremists keep trying!
But especially it would cause immense harm and lasting emotional damage, the courts found, to the children of transpeople affected. It's not 'just' a birth certificate- knowing your origins/ who your parents are is a core need in all of us- hence why adopted/ foundling children are left often with such emotional pain.
The Uk Supreme court stated not only would it be against the Gender Recognition Act, which protects these children, but also a breach of the Children Act- which protects children from emotional, as well as physical abuse. The SC declared it would be emotional abuse of children to lie about their parents and that child welfare comes BEFORE the fantasies and demands for validation from transparents.
This has now been confirmed by the ECHR. The UN Rights of the Child recognises transparents lying to children about who their parents are is a breach of international children's human rights . I have seen numerous trans activists stating every transparent should have the right to abuse their children in this way- which raises major concerns about child safeguarding and welfare, if they have a transparent this extreme. Social services need to safeguard all children, including (especially?) if they have a parent who wants to lie about this.
Useful links (posted upthread) to legal judgements:
https://childrenoftransitioners.org/paperwork/
https://childrenoftransitioners.org/six-children/
www.matrixlaw.co.uk/news/challenge-to-registration-of-transgender-man-as-mother-declared-inadmissible/