Affective polarization, defined as the dislike between opposing political groups, is a growing global threat. While much of the focus has been on partisan identities, political divisions may also be driven by affective divergence around political issues, where partisans express opposing feelings toward topics they disagree about. To compare identity-based and issue-based affective alignment, we used word embeddings to analyze two large datasets comprising ~300 million comments from partisan Reddit communities and ~7 million articles from partisan news outlets. We first quantified affective alignment by measuring the valence associations of identity and issue words. In both datasets, affective alignment was greater around political issues than around partisan identities. To validate these findings using a context-sensitive approach, we also used a large language model to rate the valence of identity and issue words in Reddit comments. We again observed stronger affective agreement around issues than identities. These results reveal that even though partisans hold strong negative attitudes toward opposing partisans, the emotional divide around political issues is less pronounced, suggesting opportunities for bridging partisan differences through issue-focused dialog. Our study offers scalable, quantitative tools for understanding the emotional dimensions of political polarization and highlighting pathways to reduce its impact.