The specific case that Obama ordered the Army to deal with was where a man had surgery to give him female breasts but still possessed penis and scrotum, but “identifying as a woman” wanted to use the female showers and toilets. The US army was ordered to comply with “her” wishes. The toilet probably doesn’t matter — each cubicle is private after all, but having to share your shower with an obviously male naked man is unfair to the normal women. Making access to gender-related facilities dependent on your stated “Gender identity” means a fully functional man could get to shower with the girls just by asserting that he “identifies” as female.
I agree with Jere on AIS women too: “these people are mentally women, and physically women, even though they are genetically men.” They are the only genetically male people who are genuinely, through no fault of their own, fully female in body and mind. Common sense says they are socially accepted as women.
Transgender gender reassignment surgery is not natural, or advisable, and should probably be illegal as it is giving concrete confirmation of the mental illness than afflicts the man who wants to be a woman. It should certainly not be taxpayer-funded. If a man thinks he’s a Bat, should the taxpayer have to fund surgery to give him wings?