Garlic, indeed it makes no sense and is caused by genderisation, as you put it.
But it has, as far as we know, been the case for thousands of years. And if women are the group that has been denied time, resources, status and attention for all that time, then the X that women do has also been denied those things, and those things are essential. So we need to change the status of both, and women benefit immediately from changing the status of X . And once society agrees those things are important and acknowledges it, and it isn't mostly women who acknowledge this, then those things get done by all not just by women.
Bella, my paragraph underneath the one you quoted explains why I think gender neutrality would be assimilation, which would be a barrier to helping the maximum number of people, and would harm them instead.
But even if that is not true, if gender neutrality doesn't logically lead to any particular priorities in society - a set of values, and it doesn't immediately improve life for many women, then it isn't as important as Beach's theory.
It is like saying I am going to paint a fence green, and abolish slavery, so everyone advocate for green fences.
While Beach's argument: We will prioritise stuff women do most because it is given low status and without freedom in a hierarchy logically has to include the end of chattel slavery. It isn't something she'll do as well. It is part of what she must do according to the argument.
Disclaimer: You can have some gender neutrality increasing at the same time as the abolition of the hierarchy and it be a good thing.
Disclaimer 2: I'm tired and this post may not explain what I mean it to.
Disclaimer 3: Beach is not actually Moses.