We studied the effects of silicon carbide (SiC) and SiC hybrid systems with different conventional fillers (silica, carbon black, graphene, hydrotalcite, halloysite) on the rheometric measurements, crosslink density, mechanical performance, aging stability, morphology, thermal behaviour, and flammability of ethylene-propylene-diene (EPDM) rubber composites. The hybrid filler systems showed technically promising synergetic effects on the performance of the EPDM composites. A pronounced reinforcing effect in EPDM composites filled with hybrid SiC filler systems was noted. Tensile strength increased in the systems with carbon black, silica, and graphene nanoplatelets, by 21%, 37%, and 68%, respectively, compared to the neat EPDM. Dynamic-mechanical analysis (DMA) revealed a shift of the glass transition temperature (Tg) of EPDM composites towards higher values following the incorporation of hybrid SiC fillers, indicating that the mobility of the macromolecule chains was restricted by the presence of filler particles. Importantly, the application of SiC as a filler in EPDM rubber composites contributed to a considerable reduction in flammability, as demonstrated by microscale combustion calorimetry (MCC). The most promising results were obtained for HAL/SiC and LDH/SiC hybrid systems, which produced final composites with high flame retardancy and good mechanical performance. The study highlights the significant potential of SiC and SiC hybrid systems as effective fillers improving the properties of elastomer composites.