*Basically intersectionality gives white women a position of privilege- they are white and a position of oppression- they are women. The privilege is the default position, and contrasts with BAME women who are oppressed in both areas.
If you refuse to recognise people who are challenging gender roles are you not, even if unconsciously, supporting established ones?*
Does anyone really get up in the morning and think 'You know what? I am going to start living my life as an Intersectionalist Feminist, and put my Third Wave views in the bin, where they belong?'
These terms are just shorthand used by sociologists to describe the ways in which feminism of the time (or in history) is being, or has been discussed. They are not series' of rules to live by.
Anyway, I agree with Galaxy that it is the idea that to conform to gender norms it is necessary to 'live as' the other gender that is not recognising people who are challenging those norms - most of us, at least some of the time, probably. Transitioning, whilst a valid choice if someone believes firmly enough in gender roles to feel the need to do it - is the ultimate in not recognising that conformity is not necessary.
I can see that for a man to remain 'masculine' and wear a dress, enjoy embroidery and 'be in touch with his feminine side' would be difficult in a lot of cases. We are not yet a society that makes that easy for most people. But we will never get there if we keep insisting that the only way to 'be female' is to do those things, and be called female. Why not just stretch the parameters of what 'being male' encompasses?