We present all-optical motionless arrangement for polarization sensitive phase-shifting (P-S) interferometry, where the phase shifts are accurately implemented by a liquid crystal variable retarder (LCVR). The LCVR is used as a polarization selective device capable of introducing a computer-controlled phase retardance between signal and reference waves with orthogonal linear polarizations. The proposed optical P-S is deployed in a polarization adapted common-path Mirau interferometer. Application of the method to a setup using the Michelson interference objective or Linnik interference module is also outlined. The accuracy of the quantitative phase reconstruction is examined theoretically, and a possibility to reduce the optical path difference error below 1/200 wavelength is demonstrated experimentally. Benefits and application potential of the polarization P-S interferometry supported by versatile liquid crystal devices are also discussed.