Gender identity is not sex. The two are entirely different things and it is not helpful to conflate them.
For the majority of people, they don't have a gender identity, they simply have a biological sex. Which is male or female. And on top of that, they have a personality that likes many different things ranging from the traditionally very feminine to very masculine. But these things are based on historical stereotypes of how men and women behave. The world doesn't look like that now, as people have more opportunity to pursue the things they prefer to do in a modern world less restrained by sex stereotypes. Thus to say one is living as a man or a woman is somewhat problematic. As it doesn't really mean anything anymore.
It doesn't matter how people dress or present. And I don't care how they do. If men want to present as what was once considered more traditionally female and women want to present as what was considered traditionally male then of course there is no issue. It's nothing surprising or particularly new.
What is important though is that gender identity is not conflated with sex. They are not the same thing. And they diminish sex based rights, services and protections.
And what is important to remember, that amongst all these different personalities and presentations, is that a woman is an adult human female. And a man is an adult human male. It is not possible to identify out of the concrete reality of what one is born as.
Instead of attempting to conflate sex and gender, it would be better to celebrate each others diversity and differences, whilst understanding that both sexes have very different needs which are central to their biological reality.