This paper demonstrates the influence of external optical feedback on the polarization state of longitudinal modes in quasi-isotropic microchip Nd:YAG lasers. Under optical feedback, the polarization state of longitudinal modes in quasi-isotropic lasers relies strongly on the intracavity anisotropy loss and mode competition. When the intracavity anisotropy loss is small, external optical feedback can cause polarization switching and strong mode competition between two orthogonal linearly polarized eigenstates of one laser longitudinal mode, which leads to the distortion of laser intensity modulation waveform. The polarization switching is independent of the initial external cavity length. By increasing the intracavity anisotropy loss, one polarization eigenstate can be suppressed and the laser works in single-polarization state. A theoretical analysis based on the compound cavity model is presented, which is in good agreement with the experimental results. The results offer guidance to the development of laser feedback interferometers.