Scholars and activists have raised alarm about affective polarization---voters' increasing dislike for supporters of opposing political parties---and its potential negative implications for democracy. Organizations, activists, and scholars have identified cross-partisan conversations as a promising paradigm for reducing affective polarization and, in turn, bolstering democratic accountability. However, existing theory and empirical work remains ambiguous. We argue that cross-partisan conversations have potential to reduce intergroup prejudices, but that such one-shot interactions are likely to have short-term effects that decay, would be circumscribed within the interpersonal domain and not extend to democratic attitudes, and would be conditional on topic, diminishing if the conversations dwell on group differences. We support this argument with results from two unique experiments where we paired outpartisan strangers in real time to discuss randomly assigned topics face-to-face over video calls. In Study 1, we found that non-political conversations between outpartisans dramatically decreased affective polarization, reversing over two decades' worth of increases. However, these impacts decayed completely in a follow-up survey. Moreover, the conversations had no effect on outcomes related to democratic accountability, such as support for outpartisan politicians. Study 2 replicated Study 1's results in a more representative sample and included conversations about group differences (i.e., politics). We again found large effects of non-political cross-partisan conversations on affective polarization, but that conversations about group differences had no effects. All conversations were again ineffective at changing democratic attitudes. Our results support our argument regarding the conditional, short-term, and circumscribed effects of cross-partisan conversations.