The Stirling engine, renowned for its high theoretical efficiency, is capable of partaking an active role in the current energy transition. Given its closed-cycle operation, the choice of the working fluid is pivotal in designing the Stirling engine. Dinitrogen tetroxide N$_2$O$_4$ has been extensively investigated in the past, based on the ideal gas thermodynamic model, as a chemically reactive working fluid for Stirling cycles. This molecule reversibly and rapidly dissociates into nitrogen dioxide NO$_2$ – and recombines into N$_2$O$_4$ - under the influence of thermodynamic transformations throughout the cycle, in accordance with chemical equilibrium. Addressing discrepancies in previous studies, this work aims at assessing a wide range of theoretical chemically reactive gases as working fluids in a Stirling cycle, employing the ideal gas mixture model. The behavior of each reactive fluid is examined throughout the cycle, and the thermodynamic performance is evaluated. Therefore, this work quantifies and analyzes the thermodynamic performance of a chemically reactive Stirling engine. Results indicate a slight increase in the net specific work output with certain reactive fluids, offering a thermal efficiency comparable to that of inert working fluids. In addition, it is emphasized that for chemically reactive working fluids, the isochoric heat exchange within the internal regenerator is incomplete due to chemical reactions, in contrast to the case of inert fluids. To address this, either a supplementary heat source, heat sink, or both are required during the isochoric processes. Furthermore, chemically reactive fluids in the Stirling engine induce irreversibility in the internal regenerator, stemming from heat exchange across a finite temperature difference, penalizing the thermal efficiency of the engine for the majority of reactive fluids studied.