This study investigates a polarization-insensitive surface plasmon resonance (SPR) sensor based on a D-shaped photonic crystal fiber (PCF) with a sinusoidally modulated surface morphology. By optimizing structural parameters including the period, amplitude, and core proximity of the sinusoidal surface profile, we systematically explore their influence on SPR characteristics and polarization-independent performance. The results demonstrate that reduced periods or increased amplitudes effectively achieve polarization independence, manifested by equal X- and Y-polarized loss peaks at identical wavelengths. Numerical simulations reveal polarization-independent operation at periods of 5 μm, 7.5 μm, 10 μm, and 12.5 μm through appropriate amplitude adjustments. Furthermore, the impacts of critical fiber parameters (air hole diameter, pitch, and metal film thickness) on SPR excitation are comprehensively analyzed, accompanied by proposed optimization guidelines. This work provides novel insights into the design of D-shaped PCF-SPR sensors with polarization insensitivity, demonstrating promising potential for diverse sensing applications.