Echo chambers in online social networks, whereby users' beliefs are reinforced by interactions with like-minded peers and insulation from others' points of view, have been decried as a cause of political polarization. Here, we investigate their role in the debate around the 2016 US elections on Reddit, a fundamental platform for the success of Donald Trump. We identify Trump vs Clinton supporters and reconstruct their political interaction network. We observe a preference for cross-cutting political interactions between the two communities rather than within-group interactions, thus contradicting the echo chamber narrative. Furthermore, these interactions are asymmetrical: Clinton supporters are particularly eager to answer comments by Trump supporters. Beside asymmetric heterophily, users show assortative behavior for activity, and disassortative, asymmetric behavior for popularity. Our findings are tested against a null model of random interactions, by using two different approaches: a network rewiring which preserves the activity of nodes, and a logit regression which takes into account possible confounding factors. Finally, we explore possible socio-demographic implications. Users show a tendency for geographical homophily and a small positive correlation between cross-interactions and voter abstention. Our findings shed light on public opinion formation on social media, calling for a better understanding of the social dynamics at play in this context.