The ancient Anatolian settlement of Catalhöyük was utterly egalitarian, drawing apparently no distinction between genders
The most recent investigations also reveal little social distinction based on gender, with men and women receiving equivalent nutrition and seeming to have equal social status, as typically found in Paleolithic cultures
A human culture that makes no distinction between genders isn’t going to last very long. Certainly no Paleolithic nor Neolithic society is going to.
A society that makes no particular gender distinctions in nutrition will do just fine.
For example, the modern UK doesn’t make any particular gender distinctions on nutrition. But I think we’d be able to get Zoe to agree that it still makes rather too many distinctions based upon gender, no?