Thank you, it is really helpful to get this insight into your thinking.
So for you, the difference between men and women is indeed that they have different types of mind rather than different types of body, because for you it is possible to that two people with identical bodies could stand in front of you and one be a man and the other a woman.
So for me this raises some further questions:
I understand "female" to be a fact of the body. Female (or woman) to me is simply the name for people who have that body type. There is no other component to it. So to me, if you take away the body from the definition of "woman" (or man) there isn't any further thing left in the term that a person could be. The concept of being "innately female" without a female body is as meaningless to me as the idea that a blue square might be "innately red".
Clearly for you this is different. In your understanding of these things what does "innately female" describe, and how does that innate female quality give rise to to the need for female-only sports, protections, opportunities etc?
And finally, why does this innate feeling need to have the name "man" or "woman" when those words already referred to body types? If Man or Woman is not a fact of the body, what's the connection between their original meaning as a fact of the body and the new meaning as a fact of the mind? And given that male and female bodies obviously do also exist and being one or the other does have material physical and social consequences, why are there not also words for the different sexes?