Robots and other artificial intelligence (AI) systems are widely perceived as moral agents responsible for their actions. As AI proliferates, these perceptions may become entangled via the moral spillover of attitudes towards one AI to attitudes towards other AIs. We tested how the seemingly harmful and immoral actions of an AI or human agent spill over to attitudes towards other AIs or humans in two preregistered experiments. In Study 1 (N = 720), we established the moral spillover effect in human-AI interaction by showing that immoral actions increased attributions of negative moral agency (i.e., acting immorally) and decreased attributions of positive moral agency (i.e., acting morally) and moral patiency (i.e., deserving moral concern) to both the agent (a chatbot or human assistant) and the group to which they belong (all chatbot or human assistants). There was no significant difference in the spillover effects between the AI and human contexts. In Study 2 (N = 684), we tested whether spillover persisted when the agent was individuated with a name and described as an AI or human, rather than specifically as a chatbot or personal assistant. We found that spillover persisted in the AI context but not in the human context, possibly because AIs were perceived as more homogeneous due to their outgroup status relative to humans. This asymmetry suggests a double standard whereby AIs are judged more harshly than humans when one agent morally transgresses. With the proliferation of diverse, autonomous AI systems, HCI research and design should account for the fact that experiences with one AI could easily generalize to perceptions of all AIs and negative HCI outcomes, such as reduced trust.