Most people associate with people like themselves, a process called homophily. Exposure to diversity, however, makes us more informed as individuals and as a society. In this paper, we investigate political disagreements on Facebook to explore the conditions under which diverse opinions can coexist online. Via a mixed methods approach comprising 103 survey responses and 13 interviews with politically engaged American social media users, we found that participants who perceived more differences with their friends engaged less on Facebook than those who perceived more homogeneity. Weak ties were particularly brittle to political disagreements, despite being the ties most likely to offer diversity. Finally, based on our findings we suggest potential design opportunities to bridge across ideological difference: 1) support exposure to weak ties; and 2) make common ground visible while friends converse.