The BBC report that birth certificates for the children of same-sex parents are now accurate, with comments from a few couples on the difference it makes.
Reading the two together makes it clear that the likes of Nadine Dorries MP (Conservative, Mid Befordshire) are objecting on the grounds that "reducing paperwork for parents is damaging family values". Dorries, is of course a pro-bigotry conservative rather than a small-government conservative, and so can support unpleasant and upsetting red tape in this instance.