What do you mean 'psychologically men'? Do you mean like 'ladybrain'? Because there is no evidence for female brains in men's bodies.
I mean that they have a psychological understanding that they are men, whether or not they are biologically male.
But they are different issues, with different roots and need different solutions. The gay or black rights movements never tried to appropriate the struggles of women's oppression, or make out they were more oppressed and than this group or that group. They are there to campaign for their rights and want to look at the root causes and solutions to their oppression. The trans movement appropriates whatever they can, to make it about themselves.
I'm sorry, but are you very well versed in history?
Of course different marginalised groups have done this to each other! Racism was rampant in the Suffragette movement. To this day, white feminists appropriate things made to highlight racism- did you see the woman who appropriated 'This is America' to make it about white women? Gay men are infamous for being misogynistic. Homophobia is and has been extremely pervasive in the black community. The list goes on and on...
Being a member of one marginalised community doesn't mean you don't have prejudices, or actively discriminate against, others. These are not the first two groups to have problems, but it appears to be coming to a head and, like I said, the issues overlap very frequently, making it difficult.
So me "feeling" like a unicorn is irrelevant.
Because you would be 'feeling' a physical thing. Gender is not a physical thing.
And what's in my head may be the most important part of me (I quite agree) but I have not been sidelined at work, or called dirty names or been physically attacked by men because of what's in my head.
You're missing the point. Sex-based discrimination is a thing - as is transphobia. Transphobia refers directly to gender, or more importantly, identifying as a gender that opposes your sex. So yes, you will experience misogyny based on your sex, and yes, trans people will experience transphobia based on your gender identity. Those two things are not incapable of coexisting as facts.
How can you have gender as a universal, objective, non stereotype, non socially constructed thing?
No, I don't mean sex.
People are beginning to reject gender stereotypes and conventions, the concept of 'gender' has not been completely erased. People are fully aware that you can identify as a woman or man and still not like shopping or sports respectively.
So, when people say they identify as a woman, they don't mean they like pink and shopping. They mean that they feel as if they are a woman. It doesn't stop them getting a crew cut or joining the army or being a CEO. But they identify as a woman.