Generative AI is altering how we work, learn, communicate, and participate in online communities. How might online communities be changed by generative AI? To start addressing this question, we focused on online community moderators' experiences with AI-generated content (AIGC). We performed fifteen in-depth, semi-structured interviews with moderators of Reddit communities that restrict the use of AIGC. Our study finds that rules about AIGC are motivated by concerns about content quality, social dynamics, and governance challenges. Moderators fear that, without such rules, AIGC threatens to reduce their communities' utility and social value. We find that, despite the absence of robust tools for detecting AIGC, moderators were able to somewhat limit the disruption it caused by working with their communities to clarify norms. However, moderators found enforcing AIGC restrictions challenging, as they rely on time-intensive and inaccurate detection heuristics. Our results highlight the importance of supporting community autonomy and self-determination in the face of this sudden technological change, and suggest potential design solutions that may help.