Blue, no idea if you will read this if you are bowing out, but...
Of course all people are equal. But not all people are the same. Men are not the same as women, that's not what being equal means. Black people are not the same as white people.
On the inside we are all the same - but society doesn't categorise people by their insides. That's what despite the fact that race is a meaningless concept in terms of actual differences, it has meaning because society gives it meaning. Being black in the UK or US particularly is more dangerous than being white in lots of ways because society ascribes certain roles to black people. Same with women, obviously.
So there are fundamental differences in the way humans are socialised and perceived on a societal level. We are therefore different in terms of our social categories, although equal.
And no, many women can't and don't accept that trans women are women in exactly the same way that we are. Biology is not imaginary, it's a real set of distinctions between male and females of any species which exist, objectively. Ascribing sex to body parts is not essentialist, it's factual.
Gender identity isn't the same as sex, it resides in the mind, not the body, but that doesn't mean that the brain (as the brain is not the same as the mind) has a gender or a sex. Both of those assertions have been made by trans theorists and they are simply untrue. The mind creates a gender identity out of its experiences in the world, how the person is treated and socialised. The gender identity can be influenced by hormones as in 'butch' as an identity that is often expressed by masculine women who tend to have higher levels of testosterone. However it isn't innate, it isn't predetermined at birth and it isn't separate from the person's lived experiences.
To say otherwise puts women back in the box where we lived when women were believed to be less intelligent, less rational, more animal, better at housework and worse at science. It validates the idea of male and female brains which is a gift to misogynists. It is self defeating and actually self hating for a feminist to accept this doctrine (because it is a doctrine, it's not fact)
Personally I am very happy to call a trans woman she, by a female name and hang out with her as a female friend. I completely accept that trans women have body and sex dysphoria and that presenting as a woman may make them feel much happier about themselves. I'm not wedded to the concept of gender so it doesn't matter to me if a male person wears dresses and makeup and heels, because I don't think those signifiers are very important. I'm not transphobic but neither do I accept, uncritically, that trans women are women the same way that I am.
I have lived through childhood as a girl, adolescence as a girl and adulthood as a woman. I have a female body and female experiences. I will not accept that I am not allowed to refer to PMT and pregnancy and contraception and vaginal penetration and clitoral orgasms as female experiences. I will not have my life being socialised as a woman devalued and made nothing by trans women asserting that their boyhoods were actually girlhoods because tada! They were female all along. I will not accept that a penis can be reframed as a long clitoris or that a penis can be female. I will not accept that calling female genital mutilation by its name is 'cissexist'. That is all bullshit to me and I will never accept it.
Im so grateful to the feminism boards for allowing me a space to think deeply about trans theory. I was in a total state of cognitive dissonance before as I was so anxious about being transphobic. I hope these threads continue until nobody wants to discuss it anymore. We have not yet reached peak trans on mumsnet - far from it.