Usually it's more about a form of unstable and contextual xenophobia.
But it's not just against people. Also about all living things, object, behavior, events...
People are label racists like it's a deep nature, while it's most likely a small symptom of poor education + a twisted defensive reaction that is bigger than that, and is not particularly linked to race.
Well, I don't agree that that is the postmodern view, unless you define "postmodern" to specifically mean that view so that it is tautologically true; particularly, I don't believe that its all that common for any person (regardless of whether the label "postmodern" applies) to hold simultaneously to both of those beliefs. They may both be beliefs that are visible in some segment of the population, and there may be some overlap, but I don't think there is much correlation.
But, in any case, even if they were commonly held together, there is nothing inconsistent in believing that all beliefs and behavior patterns are products of the interaction of the individual with the external environment, and believing that there are certain beliefs and behavior patterns that, once established, are not correctable through any change in the environment that other people can effect (even if the same behaviors/beliefs may be made less likely to manifest in those who have not already manifested them), such that those behaviors/beliefs only go away when the people holding them die.
Hence why we don't expect to successfully re-educate them, and will have to outlive them instead.
But I suspect that the nature of postmodernism means we won't really be able to resolve what views are and aren't consistent with it to any objectively satisfying degree ;-)
Serious (offtopic) metaquestion: why is the postmodern view that all people, including violent criminals, are victims/products of their environment, but racists are uniquely and irredeemably evil to their core?