How people interpret content is deeply influenced by their socio-cultural backgrounds and lived experiences. This is especially crucial when evaluating AI systems for safety, where accounting for such diversity in interpretations and potential impacts on human users will make them both more successful and inclusive. While recent work has demonstrated the importance of diversity in human ratings that underlie AI pipelines, effective and efficient ways to incorporate diverse perspectives in human data annotation pipelines is still largely elusive. In this paper, we discuss the primary challenges faced in incorporating diversity into model evaluations, and propose a practical diversity-aware annotation approach. Using an existing dataset with highly parallel safety annotations, we take as a test case a policy that prioritizes recall of safety issues, and demonstrate that our diversity-aware approach can efficiently obtain a higher recall of safety issues flagged by minoritized rater groups without hurting overall precision.