I believe that being racist means that you believe your own race to be superior to other races? What would be the antonym for racist?
There is no reason why "racist" cannot apply to someone whose prejudices are directed at their own "race" rather than another. In fact, the OED definition of "racism" inclines this way:
...a person whose words or actions display prejudice or discrimination on the grounds of race.... Also in extended use: a person who is prejudiced against people of other nationalities.
(Emphasis added.) This inverts the priority as seen in OxfordDictionaries.com:
A person who shows or feels discrimination or prejudice against people of other races, or who believes that a particular race is superior to another...
Here the autoracist (neologism alert) is the second case, rather than the first.
Basically, a racist is a racist no matter whether the despised race is one's own or that of another.