I think the fact it’s so woolly, so poorly defined, so lacking in consensus (especially from within the movement’s activists), so lacking in widespread social meaning, so inherently political and ideological means that it was not an appropriate thing for the census to be asking about in the first place.
Just because an ideology or an identity matters a great deal to a small number of people in niche areas, or is currently fashionable among young people, doesn’t make it reasonable for inclusion in a national census. You may as well start asking people what football team they support (which may structure their lives in all sorts of ways) or what musical instruments, if any, they play, or whether they identify as whatever categories and tribes of youth culture currently dominate how young people see themselves in the world.
Any of them might be reasonable research topics. But the census should be asking about the big stuff about which there’s broad societal understanding and which significantly affects national planning and policy (like age distributions or sex distributions or disability). How people feel or how they’d like to be perceived isn’t really suitable for this kind of exercise.
The amazing thing is how effectively special interest groups persuaded the government that gender identity should be treated like the standard big demographic categories. Not even just asking about what’s in the equalities act (gender reassignment) but how people want to understand themselves with gender identity ideology.