The question then becomes: would you still be a woman if you were alone on a remote island, without society of any kind?

If yes, then there is something more to being a woman than a role in society. (This can be something biological, it can be gender souls, but we've ruled out the social construct hypothesis.)

If no, then society is what makes you a woman, regardless of your opinion on your gender, and there's very little you can do to change that.