Inspired by the supporters of posthumanism and transhumanism, the discussion on the status of human and non-human individuals motivates us to explore the psychological determinants of assigning a moral status (MS) to them. The article focuses on capturing the relationship between anthropocentrism and the MS of a chimpanzee, humanoid robot and cyborg person. In exploring this connection, it introduces the concepts of mind and soul as mediating variables. Three online studies were conducted, and the statistical analyses included data from a total of 732 participants aged 15–72 who were from Poland. The research shows that for each of the three characters, anthropocentrism was negatively correlated with MS, and its influence was mediated by the attribution of mind and soul. In relation to the humanoid robot, a direct relationship between anthropocentrism and MS has also been found, which is interesting in view of the discussion regarding the criteria for MS. On the other hand, the reported results for the cyborg person, which were partly contrary to expectations, need further exploration to better understand these types of entities, especially in the context of the increasing possibilities for the technological enhancement of human beings.