I know a few transsexual TW, OP.
They don't believe that TWAW either. They recognise/feel that their life experiences through being born, growing up and socialised as male are different to mine as someone who was born, grew up and socialised as female. We've had quite candid conversations about it. More than one of them has said that if they'd just been allowed to express the 'feminine' aspects of themselves without being mocked and ridiculed (by other boys) for it and had just been allowed to be the boy they were, they probably wouldn't have transitioned.
They found solace at school with the girls who just accepted them for the person they were without reference to them getting being a boy wrong and they felt safer and more comfortable and so began to 'see' themselves as a girl as a result because that was their peer group. It's where they felt 'at home'.
They are all equally horrified with the current TWAW mantra and the violence with which women are threatened for defending their own sex.
All of them have used women's toilets over the years - largely through fear of the way they will be treated in the men's. Yet they also respect the women whose spaces they share. They have no desire to intimidate women or exert any power or authority. They simply go in, wee, brush their hair and touch up their lipstick. They know many women will recognise them as male and so they keep their heads down, don't aim to draw attention to themselves and then leave, hoping they will go unnoticed, knowing they probably were noticed and hoping that women will be reassured by the fact that they tried. They're scared to use the men's. They would welcome a third space because the whole process makes them uncomfortable. They don't believe women should be threatened and forced into accepting them against our will. They understand only too well why women might not want this.
I have encountered many TW in toilets over the years. If I catch their eye at all, I smile as I would do to an unknown woman and get on with my day. I am, however, hypervigilant for any changes in their behaviour that are more typically found in men rather than women and I don't do that when I encounter unknown women. Because I recognise the threat that males can potentially pose to women that have nothing to do with their presentation/appearance. They know this and completely understand.
They know that biology matters. They don't claim to have periods or experience the menopause. They have no issue with women discussing these, and other, aspects of themselves. They wouldn't presume to be part of it and only discuss the aspects of femininity they can share - eg the pain of high heels after a night out; make up; manicures;and getting their hair done. However, they don't consider that these things make them women. After all, I never wear heels or make up and I'm still a woman. Just not an especially feminine one.
They are angry, saddened and dismayed by this current trend and the TRAs - many of whom aren't T themselves and are just using it as a way to angrily exert authority over women. They don't believe that TWAW. They believe that TWATW.
They don't believe that males can be lesbians; they don't agree with self id for a number of reasons; they are horrified by the threats of violence and aggression towards women in the name of TWAW both because they know how it feels to be threatened by big angry men who have no respect for you and because they are aware women will come to view them as the same. They don't want women to fear them but they understand why we (now) do.
As for being treated 'like a woman' which is often (rightly) met on this board with 'how can you be treated/feel like a woman? " they all agree that 'like a woman' really only means feeling intimidated and fearful of men who may wish to cause you harm; is experienced when talking to women about things such as make up, hair and shoes that they can't typically discuss with men; happens when being objectified for your perceived woman-ness; and your voice not being 'heard'. Afterall, the trans movement aggressively silences these people as it does women.
They do not believe TWAW and they see the problem as being male violence and not that women don't include them in feminism.