I think anyone is entitled to identify themselves in any way as long as they arnt lying or deceiving others for money or gain. You could argue that as a male athlete, Bruce Jenner gained himself immense fame, power and wealth in a way he absolutely would not have been able to do as a woman. His and a lot of other people's theory is that tanswomen ARE women so doesn't that mean that he was deceiving others for money or gain? Or not.
Presumably, if you take RD at her word, she identifies as Black and would have faced enormous prejudice and possibly violence telling people she was transitioning to Black and therefore just did, without telling anyone. People appear to be perfectly happy with transwomen winning sporting events, beating women born with vaginas...
My newly radical feminist take on this is that we have our biology, which others use to discriminate against us, whether that is skin colour, sexual characteristics or whatever. Overlaid is cultural and societal expectations of behaviour, dress speech and so on.
In order to solve this whole issue, what we do is get rid of discrimination, privileged violence and all the nasty shit that goes with it. We 'allow' and celebrate anyone dressing, speaking, performing, acting any way they want, as long as they aren't hurting anyone else. Bingo, no more problems.