NameChange They can claim they are real women all they like, aside from it being factually incorrect, the problem is if laws etc reflect their belief.
Here are just a few examples, there are no doubt more.
We are still a long way off equality, women are still denied job roles due to bigotry. So in some areas we have women's only positions, if a transwoman is treated as a woman and takes one of those roles, that's one less place for a biological woman.
This isn't to say transwomen don't suffer from workplace discrimination, but given that mostly it is men creating that imbalance, it is men who should be giving up more of their spaces for transwomen - not women who have a lot less spaces to give up.
It also plays a part if we are talking medical care, right now women are allowed to request a female doctor for procedures that may make them uncomfortable if performed by a man. Eg. sexual assault victims may be uncomfortable with a man providing gynae care. Transwomen are biologically male, but if they can self declare as female and then have to be treated as such, women will run into accusations of discrimination just for asking for a bio woman to provide gynae care.
There's also the matter of domestic violence refuges, many of the women in there will be suffering trauma. Right now they have the right to not allow anyone biologically male in due to wanting to provide the best possible care for traumatised vulnerable women. Do we really want to strip this away in order?
Of course this doesn't mean transwomen shouldn't have access to refuges too, that's where campaigning for specialist refuges should come in. Especially as transwomen will have different needs, and would most likely benefit from help more aimed at them.
Then there's statistics, which seem more trivial in comparison, but get used to decide where funding/support/research is needed. So can also be skewed by including transwomen as women, better to acknowledge them seperately in order to improve the lot of both groups.
Treating them as a group with their own specific needs is not taking anything away from them. It is not erasing them. It might be hurting some of their feelings, but even if we call them women without question, the reality is they still are not biologically female. This isn't women's fault.