Tackle and Tickle
I just wondering if it is possible to be racist against your own race.
Sure.
Racism is social perceptions of biological differences (... whether those differences actually exist or not) that manifest in prejudices, discrimination or favoritism.
So, let's say we had a social perception that "all white people are thieves." That's a stereotype that I've created that now exists in society. The prejudice will have a detrimental effect on white people in society, e.g. store clerks are distrusting and rude towards all those thieving white customers, the police feel that they should keep a better eye on white people in pricey stores, and judges are going to tend to give stricter sentences to white people convicted of larceny (... after all, those whites are just going to steal again!!).
In such a society, it doesn't matter
who expresses the prejudice, but that the prejudice
exists in the first place. If a white person believes that "all white people are thieves" and thus acts or argues that the perception is true, all she is doing is supporting those prejudices. Sure, she may be white herself and I'd argue that she's a probably a victim of the prejudice, but like everyone else she's still holding a racist view.