Political conflict is an essential element of democratic systems, but can also threaten their existence if it becomes too intense. This happens particularly when most political issues become aligned along the same major fault line, splitting society into two antagonistic camps. In the 20th century, major fault lines were formed by structural conflicts, like owners vs workers, center vs periphery, etc. But these classical cleavages have since lost their explanatory power. Instead of theorizing new cleavages, we present the FAULTANA (FAULT-line Alignment Network Analysis) pipeline, a computational method to uncover major fault lines in data of signed online interactions. Our method makes it possible to quantify the degree of antagonism prevalent in different online debates, as well as how aligned each debate is to the major fault line. This makes it possible to identify the wedge issues driving polarization, characterized by both intense antagonism and alignment. We apply our approach to large-scale data sets of Birdwatch, a US-based Twitter fact-checking community and the discussion forums of DerStandard, an Austrian online newspaper. We find that both online communities are divided into two large groups and that their separation follows political identities and topics. In addition, for DerStandard, we pinpoint issues that reinforce societal fault lines and thus drive polarization. We also identify issues that trigger online conflict without strictly aligning with those dividing lines (e.g. COVID-19). Our methods allow us to construct a time-resolved picture of affective polarization that shows the separate contributions of cohesiveness and divisiveness to the dynamics of alignment during contentious elections and events.