We address dissonant stance detection, classifying conflicting stance between two input statements. Computational models for traditional stance detection have typically been trained to indicate pro/con for a given target topic (e.g. gun control) and thus do not generalize well to new topics. In this paper, we systematically evaluate the generalizability of dissonant stance detection to situations where examples of the topic have not been seen at all or have only been seen a few times. We show that dissonant stance detection models trained on only 8 topics, none of which are the target topic, can perform as well as those trained only on a target topic. Further, adding non-target topics boosts performance further up to approximately 32 topics where accuracies start to plateau. Taken together, our experiments suggest dissonant stance detection models can generalize to new unanticipated topics, an important attribute for the social scientific study of social media where new topics emerge daily.