Technologies for computer-supported collaborative learning (CSCL) are playing an increasingly prominent role in educational contexts, especially as teachers and students strive to deal with pandemic-related constraints. However, the technologies being used for collaboration on a daily basis are not sufficiently equipped to promote collaborative learning as both a cognitive and a socio-emotional process. They may even run the risk of hindering the constructive exchange of ideas and provoking disputes and negative encounters. In this squib, we argue that the field of CSCL is failing to address this risk, because our research efforts are far too scattered and siloed. We introduce a manifesto of social sensitivity: increasing interdisciplinary efforts to enhance constructively critical, respectful, and cohesive collaborations in technology-supported environments. We call for concrete actions in CSCL research that ultimately contribute to more democratic and equitable collaborations.