If someone can be gender dysphoric, why can't they be race dysphoric?

The question isn't, "Why can't they be race dysphoric?" The question is whether anyone is race dysphoric? It's an empirical question.

Gender dysphoria is a psychological phenomenon that has been observed repeatedly - over and over and over again - across cultures and nations and different historical time frames. Like being gay (though with less frequency), there have been many hundreds of thousands of people reporting this condition over the decades. It's an observed phenomenon. Countless patients repeatedly (and independently) reporting the same symptoms, over and over to different psychologists and psychiatrists in different countries and different cultures, all describing similar and consistent mental phenomenon that constitute a discrete and repeated set of symptoms and experiences - an actual psychological condition that we have labeled gender dysphoria.

We haven't seen that with race. If there had been hundreds of thousands of people in countries all around the world who were experiencing severe, oft-times unbearable, psychological trauma associated with not being the "right" race, then we might similarly identify that as a thing that exists in the world.

But we don't. That's not a thing that exists. If it existed, then we might consider how to respond to it so that we could treat people who experienced it with the fairness and respect that all humans deserve. But it doesn't exist.

Gender dysphoria is not performative. Gender dysphoria is a real, psychological feature of some people's mental composition that results in a misalignment between their internal sense of gender and their external manifestation of gender. It has been observed in patients all around the world, over and over again.