Corporate social responsibility has been intensively discussed in business ethics literature, whereas the social responsibility of private consumers appears to be less researched. However, there is also a growing interest from business ethicists and other scholars in the field of consumer social responsibility (ConSR). Nevertheless, previous discussions of ConSR reveal the need for a viable conceptual basis for understanding the social responsibility of consumers in an increasingly globalized market economy. Moreover, evolutionary aspects of human morality seem to have been neglected despite the fact that private consumers are undoubtedly human beings. In addition to that, empirical studies suggest that many consumers believe themselves to be responsible but do not act according to their alleged values or attitudes. This raises the question of what deters them from doing so. Therefore, the contribution of this conceptual paper is threefold: we (i) (re-)conceptualize ConSR in terms of a combination of a Max Weber-inspired approach (social action and the ethic of responsibility) with the social connection approach to shared responsibility proposed by Iris Marion Young; (ii) shed light on the previously neglected implications of an evolutionarily induced bounded morality for ConSR, and (iii) identify potential obstacles to socially responsible consumption, particularly against the backdrop of shared social responsibility and bounded morality. In this latter respect, the paper focuses specifically on the obstacles of low moral intensity, moral stupefaction, informational complexity, and the lack of perceived consumer effectiveness. In sum, the paper advances knowledge in the field of ConSR by using a transdisciplinary, literature-based approach.