Changing rooms - should provide individual cubicles - so again no need for separate ones for Men/Women.
I do not, personally like mixed wards in hospitals - probably due to my age. However, if someone identifies as a woman, regardless of their genitalia, then they should be in a women's ward - and vice versa.
Someone who feels they are in the wrong body for their physical gender and has declared that, has already gone through so much in the way of real trauma - they should not be pushed into more.
Outside of prisons, (which may need more careful looking at), non-one is going to claim to be another gender to the one which their body seems to place them, just in order to go to the loo, or changing room cubicle.
As for sports, no problems at participation level - I have, in the recent past, accepted into a children's girls competition a youngster who was born with a penis, but has always lived as a girl. At elite end, there are more complications, but with good will these are being gradually sorted out