This work presents a Streamline-Upwind Petrov-Galerkin (SUPG) stabilized finite element framework for predicting reacting hypersonic flows under thermochemical non-equilibrium, including both non-ionized and weakly ionized regimes. The formulation is enhanced with a residual-based discontinuity-capturing (DC) operator to robustly resolve steep gradients, shock layers, and shock-interaction features. The framework solves the compressible reacting Navier-Stokes equations coupled with additional conservation equations for non-equilibrium internal energy modes, formulated in pressure–primitive variables. For thermal non-equilibrium, the governing system includes one continuity equation for each chemical species and a vibrational-electronic energy equation, enabling finite-rate chemistry coupled to a two-temperature model. The approach is assessed on benchmark cases that validate chemical kinetics and thermochemical coupling in the presence of critical high-enthalpy phenomena. Accuracy is evaluated through comparisons with numerical and experimental data from the literature, including the hollow cylinder extended flare and double-cone configurations. Finally, we demonstrate extension to ionized hypersonic flows by incorporating a weakly ionized air model and a three-temperature non-equilibrium formulation to account for additional electron energy relaxation effects. The results indicate that the proposed stabilized FEM framework provides a robust and accurate tool for high-enthalpy hypersonic simulations spanning non-ionized through weakly ionized conditions.