The reason why the feminists on mumsnet have identified and reacted to the problem is precisely because they are feminists. They have spent an inordinate amount of time analysing the reason why women as a class have been oppressed across time and geography.
No one group oppresses another group for no reason. Transwomen are not oppressed, they may be discriminated against but that's different.
Black people have been oppressed because white people wanted to extract something from them, namely their labour. To do all the shit jobs that white people didn't want to do.
Women have been oppressed because men want to extract their reproductive, sexual and emotional labour.
People are not oppressed for no reason.
Trans people are not oppressed because no one is trying to extract anything from them.
Men have used their biological strength and male bodies to enforce female oppression. The way they have propagated this is to enforce a gender role on women that means they have only been considered fit to raise children, stay in the home and have no structural or political power.
Transgenderism as an ideology says that these roles are important. And should be upheld.
The very fact that they perform a stereotypical female role means that this is a woman's role.
It's the entire basis of a patriarchal society.
Feminists get this because they understand exactly how a patriarchy works. It's entire basis of feminism.
That's why no one cares whether a transwomen presents as woman or not. Whatever gets you over your gender dysphoria.
But when you say this is what women do you are upholding an oppressive system where women are the losers. When you say this is what women do and at the same time you do exactly what the patriarchy has always done - violate their spaces, tell them they are wrong, try to silence them, threaten them, and enforce your opinion through violence you are unequivocally mired in patriarchy.