Social sorting, the alignment of social identities, affiliations, and/or preferences with partisan groups, can increase in-party attachment and decrease out-party tolerance. We propose that self-presentation afforded by social media profiles fosters subjective social sorting by shaping perceptions of alignments between non-political and political identifiers. Unlike previous work, we evaluate social sorting of naturally occurring, public-facing identifiers in social media profiles selected using a bottom-up approach. Using a sample of 50 million X users collected five times between 2016 and 2018, we identify users who define themselves politically and generate networks representing simultaneous co-occurrence of identifiers in profiles. We then systematically measure the alignment of non-political identifiers along political dimensions, revealing alignments that reinforce existing associations, reveal unexpected relationships, and reflect online and offline events. We find that while most identifiers bridge political divides, social sorting of identifiers along political lines is occurring to some degree in X profiles. Our results have implications for understanding the role of social media in facilitating (the perception of) polarization and polarization mitigation strategies such as bridging interventions and algorithms.