Despite rapid advances in artificial intelligence (AI), people remain reluctant to delegate moral authority to AI systems. Prior research has largely explained this reluctance through third-party perceptions of AI's limited mind, while paying less attention to how stakeholders' own positions in a decision may shape such attitudes. Across three main studies and three supplementary studies (N = 2,562), we found that when stakeholder positions were made salient, disadvantaged participants showed a significantly larger increase in AI delegation preference from baseline to the position-salient condition than advantaged participants. The effect held whether positional (dis)advantage was defined by experimental assignment (Study 1), self-perception (Study 2), or pre-existing social category (Study 3). Perceived self-interest alignment mediated this effect across studies, whereas alternative explanations (e.g., perceive fairness) showed inconsistent support. Notably, position salience reduced AI aversion among disadvantaged participants without reversing it, and left aversion among advantaged participants largely unchanged.