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Many scholars, engineers, and policymakers believe that algorithmic fairness requires disregarding information about certain characteristics of individuals, such as their race or gender. Often, the mandate to “blind” algorithms in this way is conveyed as an unconditional ethical imperative—a minimal requirement of fair treatment—and any contrary practice is assumed to be morally and politically untenable. However, in some circumstances, prohibiting algorithms from considering information about race or gender can in fact lead to worse outcomes for racial minorities and women, complicating the rationale for blinding. In this paper, we conduct a series of randomized studies to investigate attitudes toward blinding algorithms, both among the general public as well as among computer scientists and professional lawyers. We find, first, that people are generally averse to the use of race and gender in algorithmic determinations of “pretrial risk”—the risk that criminal defendants pose to the public if released while awaiting trial. We find, however, that this preference for blinding shifts in response to a relatively mild intervention. In particular, we show that support for the use of race and gender in algorithmic decision-making increases substantially after respondents read a short passage about the possibility that blinding could lead to higher detention rates for Black and female defendants, respectively. Similar effect sizes are observed among the general public, computer scientists, and professional lawyers. These findings suggest that, while many respondents attest that they prefer blind algorithms, their preference is not based on an absolute principle. Rather, blinding is perceived as a way to ensure better outcomes for members of marginalized groups. Accordingly, in circumstances where blinding serves to disadvantage marginalized groups, respondents no longer view the exclusion of protected characteristics as a moral imperative, and the use of such information may become politically viable.