Cross-topic stance detection is the task to automatically detect stances (pro, against, or neutral) on unseen topics. We successfully reproduce state-of-the-art cross-topic stance detection work (Reimers et al., 2019), and systematically analyze its reproducibility. Our attention then turns to the cross-topic aspect of this work, and the specificity of topics in terms of vocabulary and socio-cultural context. We ask: To what extent is stance detection topicindependent and generalizable across topics? We compare the model's performance on various unseen topics, and find topic (e.g. abortion, cloning), class (e.g. pro, con), and their interaction affecting the model's performance. We conclude that investigating performance on different topics, and addressing topic-specific vocabulary and context, is a future avenue for cross-topic stance detection.