Here, we develop a general theory for polarization control in adiabatically-deformed metallic waveguides. It is shown that matrix-valued Berry connections govern the polarization distribution in waveguides with a doubly degenerate fundamental mode. We establish a ge- ometrical framework that correlates the type of adiabatic deformation with the polarization transformation as the wave propagates through the guide. Our key finding is that non-Abelian connections enable full polarization control, allowing any input polarization state to be trans- formed into an arbitrary output polarization state. Remarkably, we demonstrate that modes in closed non-Abelian waveguides generally exhibit a varying polarization state, dependent on the specific cross-sectional cut. In contrast, in Abelian waveguides, mode polarization remains fixed along the propagation direction.