Discussion across political divides is vital to sustain a functional democracy. We live in a world of unprecedented connection: high-speed Internet on our affordable handheld devices transcend geographic borders. Yet, an open question remains as to whether this heightened state of connectivity is indeed beneficial, or drives far-reaching wedges into the sphere of politics. However, there is a lack of significant research exploring the degree to which the topic under discussion influences participants to engage in cross-cutting political conversation in online communities. I explore whether the propensity for cross-cutting political discussion is dependent on the nature of the topic. I approach this question by comparing conversation patterns on Reddit's Change My View, a community created for the specific purpose of being challenged by those with differing opinions. The polarised subreddits analysed in this study were identified through tapping into the hivemind of Reddit's 'Against Hate Subreddits', a space where users flag potentially problematic communities. Structural topic models were used to extract underlying topics from a corpus of over 369,000 posts across these 18 communities over the three year time period of 2018-2021. The first research question employs structural topic models to exploree whether there is a topical difference between opinions put forwards to be challenged on Change My View and those discussed on 18 polarised subreddits. The second research question explores whether there is a topical difference not just in engagement, but also in the willingness to change one's perspective. The findings indicate a relationship between the nature of the topic and the propensity for cross-cutting political discussion. However, there seems to be no association between whether a topic is more likely to enter cross-cutting political discussion, and the propensity for those who do enter to change their viewpoint.