Algorithmic fairness research has largely framed unfairness as discrimination along sensitive attributes. However, this approach limits visibility into unfairness as structural injustice instantiated through social determinants, which are contextual variables that shape attributes and outcomes without pertaining to specific individuals. This position paper argues that the field should quantify structural injustice via social determinants, beyond sensitive attributes. Drawing on cross-disciplinary insights, we argue that prevailing technical paradigms fail to adequately capture unfairness as structural injustice, because contexts are potentially treated as noise to be normalized rather than signal to be audited. We further demonstrate the practical urgency of this shift through a theoretical model of college admissions, a demographic study using U.S. census data, and a high-stakes domain application regarding breast cancer screening within an integrated U.S. healthcare system. Our results indicate that mitigation strategies centered solely on sensitive attributes can introduce new forms of structural injustice. We contend that auditing structural injustice through social determinants must precede mitigation, and call for new technical developments that move beyond sensitive-attribute-centered notions of fairness as non-discrimination.