Do expand on what you mean by “living and acting as a man” and “living and acting as a women”.
I’d be enthralled to know just how exactly men and women are supposed to live and act.
That’s also a standing question.
Feel free to enlighten us.
Men and women live and act in societies. It almost never happens that someone is completely isolated from a society, and when it does happen it's terrible for their mental health. Societies have expectations of behavior, and ones that have been around for a while have developed social roles.
If a society deems hunting a male activity, then a woman who hunts is acting as a male according to the social norms of that society.
If their religion teaches that men should shave their facial hair, put on dresses and make themselves pretty to please a goddess and secure her blessings, then men who do that are acting like men in that society even though they are dressing like women.
If their society accepts gender fluidity then the gender identity they are expressing at any given time isn't necessarily the one they will always have. They might hunt as a man and take care of babies as a woman and it's all good because their society respects both sides of their gender identity.
It's not that hard to figure out the basics of gender roles in societies and how/why those roles are not strictly linked to biological sex if you really want to give it some thought.