Strain tuning emerged as an appealing tool for tuning of fundamental optical properties of solid-state quantum emitters. In particular, the wavelength and fine structure of quantum dot states can be tuned using hybrid semiconductor-piezoelectric devices. Here, we show how an applied external stress can directly impact the polarization properties of coupled InAs quantum dot-micropillar cavity systems. In our experiment, we find that we can reversibly tune the anisotropic polarization splitting of the fundamental microcavity mode by approximately 60 μeV. We discuss the origin of this tuning mechanism, which arises from an interplay between elastic deformation and the photoelastic effect in our micropillar. Finally, we exploit this effect to tune the quantum dot polarization optomechanically via the polarization-anisotropic Purcell effect. Our work paves the way for optomechanical and reversible tuning of the polarization and spin properties of light-matter-coupled solid-state systems.