Skin colour is not a social construct. Gender is. You cannot legitmately claim to be black if you are not black, IMO. You can legitimately claim to be female, whatever your biology.
Female refers to sex though, not gender? And sex isn't a social construct. Gender can be changed but sex can not.
So you can claim to be female(sex) but if someone is born male, then their sex is always male, however much it hurts.
If someone claims they are black, but was born white, then their race will awaits be white, however much it hurts.
People are still treat differently according to skin colour, sometimes it's open hostility, but sometimes it's an ingrained bias, (I'll try find links) so if a white person who has benefitted from white privilege takes a job/place intended for a black person, often created to address inequality, the black person loses out, and when many have to work so much harder to get places in higher power than someone who is white, I can see why people have a problem with a white person feeling black taking positions intended for black people.
People are still treat differently according to sex, regardless of how they feel inside, sometimes it's open hostility, but sometimes it's an ingrained bias, (I'll try find links) so if a male who has benefitted from male privilege takes a job/place intended for females, often created to address inequality, the female loses out, and when many women still have to work so much harder to get places in higher power than someone who is male, I can see why people have a problem with a male who feeling female taking positions intended for females.
disclaimer, I don't hate Transwomen, I don't want transwomen to face violence, suicide or any of the other horrible things they have to face.