If you can pick your sex, then you can pick your race. I’d like my kids to be black when taking tests or applying to colleges or for jobs. Identifying as a black woman would be ideal.
Brace yourself: when I was a civilian employee for the Air Force I worked briefly in the Civilian Personnel Directorate of my local AF base. In 2002, there were on separate occasions two white guys who came into my office wanting to change their racial classification. To my surprise, we had such a form for that purpose. They requested to be re-classified as “Native American”. I guess “white privilege” wasn’t working too well for them. Such is the Never-Never Land of the US civil service.
Why pick just one race? If you can be "gender-fluid", then why not "race-fluid" too?