But is race a physical characteristic? Well I guess different races do have different physical characteristics. When people of different races have children, then there is the understandable issue of which of the races in their mix, they most identify with. But they do have the genetic inheritance of both races.
I am Jewish. I have typically Jewish features, several very unlucky members of my family have life-limiting genetic syndromes only Ashkenazi Jews can have. I might well decide I don't identify with being Jewish and that I feel more, Somali, Japanese, Polynesian etc, but my genetic inheritance and what I see when I look in the mirror, says otherwise. Should I be able to access services open to Somalis because I feel like a Somali not a British Jew, no I shouldn't. Does it matter that I might well feel Somali, no I don't believe it does. I'm just not.
I think trans-racial is similar to trans-sexual. You may well loathe your male/female body and feel the need to change it radically, you may well identify totally with the opposite sex, you may feel you are the opposite sex but that doesn't mean you are that sex surely.