The high coherence of laser light sources is a key to the application of diffractive optics usable in holographic AR/VR displays. This can be combined with switchable diffractive elements, which are advantageous for several optical functions used in immersive holographic displays such as shutters, polarization filters, for rapid beam deflection and selection. We demonstrate a compact, effective and robust diffraction wide-angle switchable beam-deflecting device based on circular polarization gratings possessing Bragg-performances (Bragg-PG) and a polarization switch. Such grating/polarization switch pair may, for instance, be a discrete switchable deflection element or as a switching element for pre-deflection with field lenses for application in holographic AR/VR displays. Micrometer-thick circular polarization gratings characterized by high diffraction efficiency (DE > 95%), large diffraction angles (< 30°) and wide angular and wavelength acceptance were developed. In the presented embodiment, the output signal is controlled between the zero- and first-diffraction orders by the handedness of circular polarization of the incident light. Forming a stack of two such oppositely aligned gratings can double the deflection angle. These gratings are the result of a two-step photochemichal/thermal processing procedure of a photocrosslinkable liquid crystalline polymer (LCP). The holographic patterning provides a high spatial resolution (period < 700 nm) and the arbitrary orientation of the LC director as well as high optical quality and thermal and chemical stability of the final gratings. Highly efficient (diffraction efficiency, DE > 95% in the vis spectral range) and stable symmetric and slanted circular Bragg polarization gratings were fabricated using the developed material and processing technique. The high usable diffraction angles combined with high DE make the Bragg-PG attractive for HMD AR/VR applications because of the system inherent short focus lengths and large numerical apertures needed to meet the low space budget in HMD and other optical systems.