Studies on recommendations in social media have mainly analyzed the quality of recommended items (e.g., their diversity or biases) and the impact of recommendation policies (e.g., in comparison with purely chronological policies). We use a data donation program, collecting more than 2.5 million friend recommendations made to 682 volunteers on X over a year, to study instead how real-world recommenders learn, represent and process political and social attributes of users inside the so-called black boxes of AI systems. Using publicly available knowledge on the architecture of the recommender, we inferred the positions of recommended users in its embedding space. Leveraging ideology scaling calibrated with political survey data, we analyzed the political position of users in our study (N=26,509 among volunteers and recommended contacts) among several attributes, including age and gender. Our results show that the platform's recommender system produces a spatial ordering of users that is highly correlated with their Left-Right positions (Pearson rho=0.887, p-value < 0.0001), and that cannot be explained by socio-demographic attributes. These results open new possibilities for studying the interaction between human and AI systems. They also raise important questions linked to the legal definition of algorithmic profiling in data privacy regulation by blurring the line between active and passive profiling. We explore new constrained recommendation methods enabled by our results, limiting the political information in the recommender as a potential tool for privacy compliance capable of preserving recommendation relevance.