Earlier quoted context omitted.
The joke is unambiguously not a comment on the fluidity of racial identity.
The joke is mocking the beliefs of the managerial class. That’s Adams’ whole shtick. In this case his mocking the contradiction in how ideologies ascendant among the managerial class view the fluidity of race versus gender.
The article points out that Adams deeply warped personal beliefs have thus far not overtly made it into the comic strip, but not only have they now (with this strip as an example), but Adams himself is bragging about it on Twitter.
So: no, the joke here is not simply about mocking the beliefs of the managerial class. It's the "identify as an attack helicopter" joke, as a preceding comment correctly observed.