The exponential increase in the availability of genomic data, derived from sequencing thousands of loci or whole genomes, provides exciting new insights into the diversity of life. However, it can also challenge established species concepts and existing management regimes derived from these concepts. Genomic data can help inform decisions about how to manage genetic diversity, but policies that protect identified taxonomic entities can generate conflicting recommendations that create challenges for practitioners. We outline three dimensions of management concern that arise when facing new and potentially conflicting interpretations of genomic data: defining conservation entities, deciding how to manage diversity, and evaluating the risks and benefits of management actions. We highlight the often-underappreciated role of values in influencing management choices made by individuals, scientists, practitioners, the public, and other stakeholders. Such values influence choices through mechanisms such as the Rashomon effect, whereby management decisions are complicated by conflicting perceptions of the causes and consequences of the conservation problem. To illustrate how this might operate, we offer a hypothetical example of this effect for the interpretation of genomic data and its implications for conservation management. Such value-based decisions can be challenged by the rigidity of existing management regimes, making it difficult to achieve the necessary flexibility to match the changing biological understanding. We finish by recommending that both conservation geneticists and practitioners reflect on their respective values, responsibilities, and roles in building a more robust system of species management. This includes embracing the inclusion of stakeholders in decision-making because, as in many cases, there are not objectively defensible right or wrong decisions.