Personal assistance robots are making inroads into our private and public life. At the same time, most humans are still unfamiliar with this technology and hesitate to accept and use it for daily tasks. Fortunately, the designs of robots can be adjusted to yield greater acceptance, subsequently enabling their utilization across various tasks. Using a scenario-based online experiment, we explored how sociability (low vs. high), ownership (private vs. public), and affinity for technology influence the acceptance and intention to use a robot for grocery shopping. Moreover, to assess users’ preference for robots’ morphology, participants were asked to choose a robot (technical vs. anthropomorphic design) that they would prefer to use in a supermarket. We found that low sociability of the service robot and a higher affective affinity for technology led to a higher level of acceptance. For more sociable robots, higher levels of anthropomorphism were preferred. Our results point to the importance of task-specific robot design that exceeds functional considerations.