Skaven society might very well be "beyond" gender (theory/discussion)
As in, it's fully plausible for female skaven to exist in skaven society outside of the rat mothers. TLDR: skaven only care about themselves and don't give a shit about categorization because it doesn't help them personally and rat mothers don't only give birth to males.
The only piece of lore that directly contradicts the existance of non-male sexes in skaven society (atleast to my knowladge) are a few passages from Warhammer FRP - Children Of The Horned Rat - 2nd edition, namely "There are no skaven females, only skaven broodmothers" and "Female skaven serve no other purpose other than to propagate their vile species (...)". But even in this very book there is some slight apprahension; "These (...) baby factories are the only female skaven known to exist".
The main point of this theory boils down to the fact that skaven are simply to egocentric and focused on their own survival and advancement in the skaven hierarchy to give a shit about gender as we know it. The one and only thing the overwhelming majority of skaven care about (rare exceptions could be things such as the Queek/Ska (b)romance etc.) is themselves. No skaven would give a rat's ass (pun intended) about social categorization based on arbitrary physiological and biological attributes unless it wouldld benefit him and only him.
Speaking of biology, many of the of the potential physiological differences between sexes that could lead to propagation of a gender binary (potentially differing musclemass etc.) would be nullified by the fact that the vast majority of skaven exist in a state of perpetual malnourishment. I also find it unlikely that the aforementioned rat mothers/breeders would give birth to almost exclusively skaven of the male sex. Assuming that rat mothers give birth to equally as many females as males, it is plain to see that if all females were turned into breeders the resources required to feed and nurture both them and their litter would be completely unsustainable. where would these females then go? Out into the gender-free skaven society with everybody else, of course.
The fact that skaven are referred to, both by themselves as well as all other races, using gendered pronouns (he/him) is also worth bringing up. I find the explenation to this to be quite simple. Whenever we read dialouge from skaven in novels or any other source material, it is translated into english (or whatever language, really) from their own radically different language. Usage of gendered words such as "he" could simply be the best adaptation of the skaven language based on our human preconceptions, without necissarily implying a gender on the skaven referred to. As for other races referring to skaven using gendered pronouns I find the explenation to be even simpler. On a societal level these races only come into contact with the martial side of skaven society, the warriors and soldiers (there are obviously instances of individuals contacting and talking with other facets of skaven society, such as grey seers etc.). These races then apply their own experiences of martial matters (i.e as something masculine) to skaven and thusly, masculine pronouns are applied to the whole of skavendom.
In conclusion, skaven live in a genderless society inhabited by more than a single sex. Atleast that's how I interpret them. I hope I made my thoughts clear. If you feel i missed something or have any questions, don't fret to tell me. Thanks for reading!