Regarding your question: "If gender can be separable from biological sex, why can’t race be unhinged from biological pigmentation?" The short answer is: Because the social constructs of gender and race work differently from each other in this respect. The social constructs "could" have developed differently in the past and "might" develop differently in the future, but, right now, gender works one way and race works another way.

Gender and race just ARE different. Anyone could make a list of the ways in which they are different. I, however, find it extremely unproductive to do so, especially in this context—specifically, in the context of discussions about Rachel Dolezal, Richard Dawkins' antagonistic tweet against transgender people, and the general tenor in which you posed your question.

In 2017, there was a brief philosophical discourse about why-can't-you-change-your-race-just-as-you-can-change-your-gender, as I mentioned in my article. Again, I am deliberately choosing not to engage that discourse on its own terms. There are reasons I do not want to answer that question.

When white people claim to be Black, it is harmful—not just inconvenient, but harmful—to Black people. My article provided links to eight articles by Black authors who have explained why. I do not want to explain this myself, in part because I am not Black and I am not the best person to represent those experiences, feelings, beliefs, and arguments. You would do much better to directly read the articles that Black people have written.

I wrote this article, "Why Did Richard Dawkins Tweet About Rachel Dolezal?," to provide historical background for another, longer article that I posted immediately afterward. That second article, "How Did Richard Dawkins Undermine Transgender People?," explains how Dawkins referenced the 2015 Dolezal story in a 2021 tweet. https://aninjusticemag.com/how-did-richard-dawkins-undermine-transgender-people-b38dcfe1a2e7

I split them up into two articles just so the size would be more manageable. Each article contains a link to the other. If you don't continue on to read the second article, you may not understand what motivated me to write the first one.

On the other hand, if you are "not all onboard with this transgender thing," then you probably won't like my second article, either.