When is speech on social media toxic enough to warrant content moderation? Platforms impose limits on what can be posted online, but also rely on users’ reports of potentially harmful content. Yet we know little about what users consider inadmissible to public discourse and what measures they wish to see implemented. Building on past work, we conceptualize three variants of toxic speech: incivility, intolerance, and violent threats. We present results from two studies with pre-registered randomized experiments (Study 1, $ N=\mathrm{5,130} $; Study 2, $ N=\mathrm{3,734} $) to examine how these variants causally affect users’ content moderation preferences. We find that while both the severity of toxicity and the target of the attack matter, the demand for content moderation of toxic speech is limited. We discuss implications for the study of toxicity and content moderation as an emerging area of research in political science with critical implications for platforms, policymakers, and democracy more broadly.