Well that all depends on our definitions.

My definition of racism is a society-wide preference either for one racial group or against a racial group. In this model, the US is clearly a racist country--whites as a whole receive a preferential number of privileges than people of color from the society. Any individual within that society that benefits from that system that does not actively attempt to correct the imbalance would be perceived as "racist" to me. This definition means that in America a person of color cannot possibly be racist by having a negative cultural view of whites; however that view can be considered racially prejudiced and any action taken on behalf of that prejudice can be considered racially discriminatory.

To translate this to a smaller scale: imagine you live in a small communal society of 20 people. 10 people, for whatever reason, are designated as being superior to the other 10. These 10 superiors get twice as much food while working half as hard as the inferiors and they also get to direct the work of the inferiors so as to be preferential to the superiors. The superiors control how the commune is educated and they tightly restrict the inferiors' access to education and they distort history to highlight the superiors' "intrinsic" superiority.

If one of the superiors remarks, "I fucking hate the inferiors; they're all lazy pieces of shit and they're less than human," that could be referred to as being classist. The remark is a generalization that supports the social construct that places the superiors on top and the inferiors on bottom. As an inferior, you might say, "Wow, those superiors are all fucking assholes and I hope they all die." Is this classist? Aren't you just a little bit justified in hating the superiors? We can definitely describe that view as being anti-equalitarian and I think we all agree that the nobler goal is total equality, but can we actually fault you for your hatred of the superiors, who treat you like shit for their own benefit? Again, I'm not saying that counter-inequality is acceptable; but aren't the superiors the ones that are maintaining the dominant system of inequality and therefore more accountable for creating an atmosphere of contempt?

Edit tl;dr: POC vs. white: not racist (doesn't support the social system), but racially motivated. White vs. POC: racist (supports the social system) and racially motivated.