The legal ramifications of not having lesbian parents on BCs is a lot more complex and the issues with stigma in daily life when women or men are not represented on their child’s BC are much more intense and different from each other than some posters seem to be giving credit for.
Sperm donors (legal ones not randoms off the internet) have never been represented on BCs whether to straight or gay or married or single people so that’s a different question.
There has been loads of discussion around BCs on the Freddy McConnell court challenge to BCs threads, if people are interested.
Bottom line though most relevant to the thread title is that there is no reason not to have two women on the birth certificate when they are bringing up a child together.
That is unless you think two lesbians should not be bringing up their kids together, as apparently the Italian PM does? This issue is about lesbophobia, which has nothing whatsoever to do with identity politics. Nor surrogacy which I think is awful.
Also, if you are advocating for kids to have to have their genetic parents shown on their BCs when donor conception is used, then you are extremely naive. That would be massively invading their and their parents’ personal and medical privacy, not to mention making a proportion of women and children at risk of domestic violence and homelessness if non-paternity (which can obviously apply to consensual and non consensual sex) is shown. That’s not a win for women and children or safeguarding.