The prevalent perspective in quantitative research on opinion dynamics flattens the landscape of the online political discourse into a traditional left-right dichotomy. While this approach helps simplify the analysis and modeling effort, it also neglects the intrinsic multidimensional richness of ideologies. In this study, we analyze social interactions on Reddit, a social news aggregator and forum platform, under the lens of a multi-dimensional ideological framework: the political compass. The Reddit chosen communities for the present study are /r/PoliticalCompass and /r/PoliticalCompassMemes, two communities dedicated respectively to discussing political views through two-axis ideologies and humorous commentary on such ideologies. Given a rich dataset of over 8 million comments posted, we aim to investigate the way interactions on social media align with a fine-grained characterization of users in terms of their ideological coordinates and demographic features.