A room temperature polariton condensate realized in a microcavity with embedded GaN quantum wells emits linearly polarized light at threshold with the plane of polarization pinned to one of the crystallographic axes. With increasing pumping power, a depinning of the polarization is observed resulting in a progressive decrease of the polarization degree of the emitted light. This depinning is understood in terms of polariton-polariton repulsion competing with the static disorder potential effect. The polarization behavior differs from that of conventional lasers where the polarization degree usually increases as a function of pumping power.