The "We Are Not Trayvon" tumblr has a point, which is to remind us of white privilege. It's an important, and subtle concept. White privilege is not, as New York Times reviewer Jon Caramanica described it recently, "the belief in the normative nature of whiteness." It is not a belief at all, but instead has to do with the concrete ways in which society treats human beings differently on the basis of their race. Privilege manifests itself in whether or not you are safe from violence or protected in your perpetration of it. Whether you will be viewed with suspicion or with sympathy, irrespective of what you have done. Whether your professed fears will count as exonerating evidence in a murder trial, because they are accepted as a legitimate version of reality, or whether they will count as evidence of your complicity in your own death.
In other words, white privilege is part of the functioning of racism, which is not primarily a psychological phenomenon (like a virus that infects the soul), but the actual subjugation of human beings through legible structures of domination, including a criminal justice system whose main purpose is to protect white property and criminalize black men.