The existing literature on donor screening in transfusion medicine tends to distinguish between social concerns about discrimination and medical concerns about safety. In this article, we argue that the bifurcation into social and medical concerns is problematic. We build our case on a qualitative study of the historical rise and current workings of safety practices in the Danish blood system. Here, we identify a strong focus on contamination in order to avoid 'tainted blood', at the expense of working with risks that could be avoided through enhanced blood monitoring practices. Of further significance to this focus are the social dynamics found at the heart of safety practices aimed at avoiding contamination. We argue that such dynamics need more attention, in order to achieve good health outcomes in transfusion medicine. Thus, we conclude that, to ensure continuously safe blood systems, we need to move beyond the bifurcation of the social and medical aspects of blood supply as two separate issues and approach social dynamics as key medical safety questions.