Something else occurred to me. Humans are predisposed to role play, act, make believe. Story telling, song, dance, acting, are all about telling a story and the audience suspends their disbelief. Humans have pretended to be people and sometimes animals for all of eternity. Think about fairy stories - they are full of people changing form or pretending to be something they are not. Sometimes it is to con others, sometimes for fun, sometimes to achieve an aim. There will always be a few rare and remarkable cases in which people take things to a new level e.g. the case of Sacheen Little Feather, the famous Native American activist who has been revealed after her death to be of Spanish-Mexican descent, or Anna Delvey who convinced many people that she was an heiress until she was found out. But these are so rare they do not have great cultural or social significance.
Also, men have always dressed as women, women have always dressed as men in the theatre, for fancy dress, drag, fetish, comedy. It's part of our culture. But people have always known where to draw the line.
What has changed is the internet. We know that Men + sex + the internet is having a great effect on our society. Online communities and the proliferation of porn are creating larger communities of men with the same interests. They have found each other and drawn others in. This gives them power and the confidence to push boundaries, to break taboos, to expose what would once have been behind closed doors. No other group of 'impersonators' is such a large homogenised group with such a strong motivation.
Role playing is a game humans have always played and Gender Ideology is a game. I believe those playing the game, know that this is the case and are pushing it further and further. It began as going out 'dressed as a woman' along a continuum to 'changing the law to say that I am a woman and anyone who says I am not will be vilified' They are seeing who they can manipulate to play along. They are having fun with the contradictions. Think of all of the amazing contradictions here:
A man in a dress is a woman and yet EVERY other form of cultural appropriation or assumed 'identity' as addressed here, is social death.
There are women who join violent, aggressive men protesting against feminists
Charities set up to promote gay rights advocating for the sterilisation of children and bullying of lesbians
Women who oppose young women having double mastectomies being told they are fascists
Schools throwing safeguarding out of the window
Victims of crime, courts, having sworn an oath to tell the truth, being ordered to refer to their rapist as 'she'
Children being told that parents who love them and tell them they are perfect are hateful bigots
Victims of male violence being told by the organisations set up to support them that they must accept males in their sanctuary and reframe their trauma
Intelligent, well educated, experienced politicians being totally flawed by a simple question about whether a rapist is a man or a woman or whether only women have a cervix.
So a very long winded way to say, OP, that the answer to your question is that yes this is a massive contradiction and that's the point - it is all part of the game.