Interspecific hybridization is one of the most controversial—and usually neglected—issues in conservation due to its multiple evolutionary consequences that might include the origin and transfer of adaptations, the blur of distinctive lineages or the formation of maladaptive hybrids. However, despite different outcomes, most conservation laws do not offer any possibility of hybrids being protected since they are perceived as a threat to the survival of pure species. We assessed how much hybridization has contributed to species extinction considering all IUCN Red Data assessments. However, we found that it has been scarcely reported as a threat contributing to extinction: only 11 extinct species out of 120,369 assessments mentioned hybridization. Although the causes that contribute to species extinctions should be controlled, the reasons for not conserving hybrids seem subjective rather than empirically supported. In a genomic era where hybridization is being more frequently detected, the debate involving the conservation of hybrids should be re-opened. Should we conserve hybrids despite the possibility of gene flow with parental species? Should we protect only natural hybrids? The resolution of this debate goes to the heart of what we mean to conserve and the time scale of conservation. But hybridization is part of the evolutionary process and might even increase in the future due to human-induced changes. As such, it becomes clear that we need to move beyond the causes and instead tackle the consequences of hybridization to create environmental policies for the management of hybrids, considering both positive and negative consequences.