Female poverty is ultimately based on the combination of sex and gender roles and sexism. The gender identity ideology tries to erase sex and also our ability to address sexism and it argues that gender roles are a good thing or at least doesn't care about them.
Women fall into poverty partly because of their role in reproduction (which is biological) and what that does for their 'employability' (my word?).
Employers don't want workers who might suddenly want maternity leave because replacements must then be hired and trained, and employers are less likely to promote and train young women because the latter are more likely to leave than young men for biological reasons.
This is made worse when the social division of labour is added in which it is still expected that women do most or all of child care and the care of elderly or ill family members.
That makes it even less likely that women are seen as good promotion candidates as the employers fear that they will be taking time off more for the sake of their children or others in the family.
And women who drop out of labour force for these reasons lose out on some pension benefits and also gain less experience in the labour market so that if they return to work later their earnings will be permanently lowered from the path they would have taken otherwise.
Sex differences (innate or learned or a combination) and gender roles (in some combination) are also why we tend to find women-dominated occupations pay less, and because they are low-paying occupations filled with many women, their lower pay translates into lower average female earnings overall.
Sexist (and sexist-cum-racist or sexist-cum-ageist etc.) assumptions in general and sexist gate-keeping in many male-dominated occupations (where women are kept out of better-paying jobs they could actually do quite well) make all this worse. Etc.
Discussing any of this requires that we define 'women' as 'people of the female sex', though some transgender women might also be hit by the same discrimination at work if others assume they are biologically female.
The gender identity ideology cannot express any of this with any clarity and could only address some of it as lots of separate and unrelated incidents. And it has nothing, really, to say about the religious and cultural discrimination which many girls face and which leaves them less education and less able to work at all.