Racism as tribal warfare vs. racism as structural oppression
1. Florida neighborhood watch member George Zimmerman chases down Trayvon Martin, a local black teenager. There is a confrontation of some sort (the details are disputed) that ends with Zimmerman shooting Martin dead. Zimmerman is widely accused of racism, but some of his defenders insist that this isn't about racism because Zimmerman is Hispanic*.
2. To raise awareness about female circumcision, Swedish performance artist Makode Aj Linde bakes a cake in the shape of a caricatured African woman's body, with his own head as the cake's head. The cake is served at a Swedish museum event, and Linde screams every time attendees cut pieces from the cake's genitals. Linde is widely accused of racism, but some of his defenders insist that he's not being racist because Linde himself is black.
The question of whether Zimmerman and Linde's races matter -- or to be more precise, whether they make the men's actions less racist -- seems to me to reveal the difference between two conceptions of what racism is. Zimmerman and Linde's defenders see racism in terms of tribal warfare, whereas their critics see racism in terms of structural oppression.
The conception of racism as tribal warfare says that racism is about one group of people attacking another group, and in particular white people attacking black people. Under this conception, something can only be racist if it is done by a member of the dominant race against another. Thus Zimmerman and Linde are off the hook in terms of racism, because since they're not white they can't be part of a white attack on black people. Their actions are at best a sort of "own goal" in the game of life, not a case of cheating by the other team.
The conception of racism as structural oppression says that racism is really about social systems that unfairly harm and limit people of some races relative to others. This system consists of behavior patterns and narratives that target certain races, but which in principle can generally be operated by people of any race. Certainly people of color have greater self-interested reasons to recognize the existence of these structures and to avoid participating in them than do whites, but the structure exists and creates racial inequality regardless of who is operating it.
In Zimmerman's case, the structure consists of the practice of directing violence toward young black men wearing hoodies on the assumption that they're up to no good. This is a racist structure because it harms black men, regardless of the race of the operator. Zimmerman took up this structure and participated in it by making racially biased assumptions about Martin that led him into a violent confrontation. And in doing so, he both perpetuated the structure's negative impacts by killing Martin, and reinforced the existence of the structure itself by providing an opportunity for spokespeople of the wider culture, such as Bill O'Reilly and Geraldo Rivera (who is also Hispanic!) to reaffirm the reasonableness of the black-men-in-hoodies-are-dangerous principle.
Likewise, Linde's art drew on a set of racist narratives that harm African women, such as the caricature on which the cake was based and the treatment of female circumcision as simple barbarism from which Westerners must rescue African women. These narratives were repeated and reinforced by Linde's art, continuing their negative impact on African women regardless of the fact that they were being repeated by a black man.
*There's some dispute about whether Zimmerman being Hispanic necessarily makes him not white -- for the sake of argument, I'm approaching this post under the scenario of "what if we take Zimmerman to be non-white" in order to illustrate my point about how we think about race.