Intersectionality is the analysis of Feminism recognises that women as individuals suffer oppression due to membership of more groups than just Women, in particular race, and that not only do women suffer alongside men as members of marginalised groups, but also that the sexism they suffer as women is shaped by the intersection of those groups and so takes a different form to women not in those groups.
As I understand it, the gender ideological view is that humans are men or women (or other genders) because of something in their mind rather than their body, and therefore male bodied people with a gender identity of woman are “real” (whatever that means) women and should be treated as women in all ways, including having their experience of womanhood included within feminism.
And that analysis of intersectionality is extended by some to include trans women as women suffering oppression in the intersection of woman and transgender, while so-called “cis” women do not have that additional oppression due to being trans.
But so-called “cis” women are by definition female-bodied. And whether you believe that biological sex is a real thing or just some colonial construction, you cannot deny that culturally it has been extremely significant whether ones body is female or male, to the point where the female half of the species has been seen as literal property of the male, body and soul, disempowered in law and in practice.
So given that history, surely even those feminists who see trans women as women with an intersection of oppression must also recognise that women with female bodies suffer the intersectional oppression of Woman and Female, and therefore Feminism that is truly intersectional must recognise the needs of female-bodied women as valid and not always aligned with male-bodied women.
It simply is not valid to say you care about intersectionality when it comes to trans women but ignore it when it comes to the huge axis of historic oppression that is physical sex.