Simultaneously pursuing social and economic value, social entrepreneurship (SE) builds on hybrid organisations that need to align competing institutional logics. But what influences this alignment? Despite digitalisation's growing importance, there is no systematic analysis of how digitalisation influences SE's hybridity, that is, its social and economic logic and their compatibility. To address this gap, we first operationalise SE's digital orientation as a matter of digital depth and digital breadth. We then briefly illustrate the positive and negative effects of digitalisation on social and economic value creation. Our findings then identify nine specific forms of how digitisation can affect SE's logic compatibility in positive, negative, and neutral ways. For future research, our discussion presents initial suggestions for measuring SE's digital orientation, provides a Weberian ideal type definition of digital social entrepreneurship, and invites investigating the institutional implications of digitising SE.