I see gender identity as having more to do with the brain and how it is structured rather than genetics. So gender is primarily mental and psychological, but with a biological basis behind it. If you talk purely genetics then yes, we aren't the same there, but gender dysphoria is when the brain and body don't align properly. I think for all the things that matter, I should be treated the same as a cisgender woman like you.
When I first started transitioning, I used the restroom that best fit my presentation at the time. I was afraid to use the women's room until I felt like my presence wouldn't cause a problem anymore. So I do agree with that, to use the restroom that best fits your gender expression. But I also think we should be equal in sports and prisons as well.
Research has been showing that with long enough on HRT, the physical differences between trans and cis women become minimal. I can personally attest to that after having been on HRT for 3 years. I wanted to post a link to some research but I don't have enough posts apparently, so the researchers name is Joanna Harper.
So I agree with IOC regs on trans players. And we shouldn't be segregated in prisons unless we can be shown to be a danger to the rest of the population (like with sex offenders and rapists).
I don't think you answered the question.
What does it feel like to be a woman? What does being a woman feel like? What does it mean to be a woman?