This depends on how you are defining racism. The actual definition of racism is to feel that your race is superior than others. You can not believe that your race is superior to itself. You can be discriminatory against your own race and make negative generalizations about your own race - these things are often viewed by society as racism, instead of the actual meaning of the word.
In your example you give a person that is of 'mixed race' (but who among us is not). In Mexico there is racial discrimination equal to or exceeding what you would find in North America. The discrimination is said to be from the light skinned Mexicans towards the dark skinned Mexicans. I am not sure what makes a Mexican more or less light skinned, but this divide exists among people thought to be of the same race.
If your race is mixed, you could feel that one race is superior to the other. In that example of Obama, he would feel that black people are superior to white people (I am not saying I believe he is this way, I am just using the example you gave). If so he is racist, but in turn believes himself to be a mix of a superior and inferior race.