Administrative registry data can be used to construct population-scale networks whose ties reflect shared social contexts between persons. With machine learning, such networks can be encoded into numerical representations -- embeddings -- that automatically capture an individual's position within the network. We created embeddings for all persons in the Dutch population from a population-scale network that represents five shared contexts: neighborhood, work, family, household, and school. To assess the informativeness of these embeddings, we used them to predict right-wing populist voting. Embeddings alone predicted right-wing populist voting above chance-level but performed worse than individual characteristics. Combining the best subset of embeddings with individual characteristics only slightly improved predictions. After transforming the embeddings to make their dimensions more sparse and orthogonal, we found that one embedding dimension was strongly associated with the outcome. Mapping this dimension back to the population network revealed that differences in educational ties and attainment corresponded to distinct network structures associated with right-wing populist voting. Our study contributes methodologically by demonstrating how population-scale network embeddings can be made interpretable, and substantively by linking structural network differences in education to right-wing populist voting.