High-entropy materials, which contain at least five metal elements, are promising catalysts for thermocatalytic applications. They offer an unprecedented diversity of surface atomic arrangements that yield highly efficient and often unexpected active sites. However, the profound influence of the support material on the reaction kinetics and stability of high-entropy nanoparticles (NPs), and thus their catalytic performance, remains a critical and elusive factor. To evaluate these support effects fundamentally, we selected conventional TiO2 and advanced, non-oxide layered h-BN. Comprehensive structural and surface chemical state analyses before and after the catalytic reaction provide insights into the structure-property relationships and the formation of new active phases such as Co and Ni enriched alloys. CO2 conversion, product selectivity, stability, and reaction kinetics are systematically studied. Furthermore, density functional theory modeling is used to elucidate the role of different metal components in CO2, CO, and H2 adsorption. The selected support materials significantly influence the catalytic properties of HEO NPs and the reaction pathways (Sabatier process vs. RWGS reaction). Unsupported HEO NPs exhibit excellent inherent stability and high CO2 conversion. Their TiO2-supported counterparts initially match this performance but subsequently suffer rapid deactivation, concomitant with a product selectivity shift from CO to CH4. In contrast, the h-BN-supported system requires a distinct activation period to overcome initially subpar performance, after which it achieves rapidly increasing conversion. Our findings highlight the remarkable potential of HEOs in thermocatalytic CO2 reduction, demonstrating exceptional conversion efficiency and stability, setting a new benchmark for next-generation catalytic systems.