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The social integration of artificial intelligence (AI) poses fundamental challenges to value-driven domains such as education, where the adoption of new technologies raises not merely technical but also deeply rooted ethical and identity-related questions. While dominant technology acceptance models (e.g., TAM and UTAUT) primarily focus on cognitive-rational factors (e.g., perceived usefulness), they often overlook the cultural and value-based elements that fundamentally shape adaptation processes. Addressing this research gap, the present study examines how two hitherto under-researched factors—religiosity and teacher’s sense of calling—influence teachers’ attitudes toward AI and, ultimately, its adoption. The research is based on a survey of 680 Catholic secondary school teachers in Hungary. To analyse the data, we employed structural equation modelling (PLS-SEM) to examine the mechanisms of influence among religiosity, sense of calling, and AI attitudes. The results indicate that neither religiosity nor a sense of calling exerts a significant direct effect on AI adoption, and their indirect effects are also marginal. Although statistically significant relationships were found—stronger religiosity reduces a supportive evaluation of AI, while a higher sense of calling increases AI-related concerns—their practical significance is negligible. The study’s main conclusion is that successful AI integration, building on teachers’ pragmatic attitudes, is achieved not by neglecting value-based factors, but by developing critical AI literacy that treats technology as a responsible amplifier of pedagogical work. This finding suggests that value-based extensions of technology acceptance models should be approached with caution, as the role of these factors may be more limited than theoretical considerations imply.