I know it’s an old and hackneyed point but I always go back to it. Suffragettes fought *against* the notion of sex based rights; sex based rights were the ones men had and women didn’t. It was seen as appalling to deny people rights based on their biology.
SilentbobReality check: "Women's hard won rights": - did NOT include defining women by biology, the slogan was "biology is not destiny!" - did NOT seek sex segregation, they fought for inclusion of women - did NOT advocate "sex-based rights", they fought AGAINST that and FOR equality regardless of sex