The growing inclusion of renewable energy sources (RESs) into power grids poses significant challenges for maintaining frequency and voltage stability. This paper investigates the effectiveness of a Fractional Order Proportional-Integral-Derivative (FOPID) controller optimized by the Mountain Gazelle Optimization (MGO) algorithm for frequency and voltage control in a hybrid power system (HPS). The proposed MGO-FOPID controller is compared with conventional Proportional-Integral-Derivative (PID) and Proportional-Integral (PI) controllers optimized by Artificial Lion Optimization (ALO), Differential Evolution (DE), and the standard MGO algorithm. The comparative analysis employs a MATLAB/Simulink model of an HPS. Performance metrics such as frequency and voltage deviations, settling times, and controller effort are evaluated under various operating conditions, including sudden load changes. The results demonstrate that the MGO-FOPID controller performs better than the other controller-optimizer combinations. It achieves faster settling times, more minor deviations in frequency and voltage, and reduced controller effort. Additionally, the MGO algorithm proves to be a robust and efficient optimizer for the FOPID controller, outperforming ALO, DE, and the standard CASO in terms of solution quality.