Algorithmic fairness has conventionally adopted a perspective of racial color-blindness (i.e., difference unaware treatment). We contend that in a range of important settings, group difference awareness matters. First, we present a taxonomy of such settings, such as in the legal system where it can be legally permissible to discriminate (e.g., Native Americans sometimes have privileged legal status, men enter the compulsory draft in America while women do not). Second, we present a benchmark suite that spans eight different settings for a total of 16k questions that enables us to assess for difference awareness. Third, we show that difference awareness is a distinct dimension of fairness and that existing bias mitigation strategies may backfire on this dimension.