Prior research on the impact of mandatory quotas in one dimension of diversity, on other dimensions, shows contradictory results. We seek to resolve this puzzle by relying on theory in social psychology on homophily and recategorization processes in hiring. In the context of a law mandating a gender quota on Indian boards, we predict and find that boards respond to the law by hiring new women directors who are similar to existing directors in terms of caste and community dimensions. We find that this homophily effect is impactful to the extent that even high-status women directors cannot overcome it. At the aggregate level, these organizational-level practices result in caste and community inequalities remaining intact despite the introduction of 1309 new women directors. We contribute to research on inequality, board of directors, and affirmative action.