Cleaning up carbon monoxide (CO) in water gas shift feedstocks is crucial for fuel cell applications. The catalytic transformation of CO in hydrogen-rich feeds poses a significant challenge in environmental catalysis. To address this issue, a range of Cu–Mn-based monometallic and bimetallic catalysts with diverse supports (such as alumina, silica, zirconia, and titania) were employed. Temperature programming techniques were utilised to observe the reduction and oxidation behaviours of these catalysts. The investigation involved testing CO oxidation at various temperatures over copper and manganese-based supported catalysts in the presence of H2O and CO2 (simulating realistic conditions). A positive impact of H2O on catalytic performance was noted, whereas CO2 had a suppressive effect. Furthermore, the specific support materials (Al2O3, SiO2, TiO2, and ZrO2) were studied to understand their roles in CO oxidation under realistic conditions. In the presence of water, alumina catalysts containing bimetallic metals (Cu–Mn) exhibited 100% CO conversion even at a lower temperature of 160 °C. Conversely, under the predominant influence of CO2, alumina catalyst (Cu–Mn) showed 55% CO conversion. The exceptional performance was attributed to CO preferential adsorption on highly active Cu–Mn sites and a small H2-oxidative atmosphere of the catalysts. The activity results highlighted the strong dependence of CO conversion on reaction temperatures, the presence of metals, and the types of supports. Overall, these findings suggest the potential use of these catalysts for H2 purification under realistic conditions.