Anisotropy plays a key role in science and engineering. However, the
interplay between the material and engineered photonic anisotropies has hardly
been explored due to the vastly different length scales. Here we demonstrate a
matter-light hybrid system, exciton-polaritons in a 2D antiferromagnet, CrSBr,
coupled with an anisotropic photonic crystal (PC) cavity, where the spin,
atomic lattice, and photonic lattices anisotropies are strongly correlated,
giving rise to unusual properties of the hybrid system and new possibilities of
tuning. We show exceptionally strong coupling between engineered anisotropic
optical modes and anisotropic excitons in CrSBr, which is stable against
excitation densities a few orders of magnitude higher than polaritons in
isotropic materials. Moreover, the polaritons feature a highly anisotropic
polarization tunable by tens of degrees by controlling the matter-light
coupling via, for instance, spatial alignment between the material and photonic
lattices, magnetic field, temperature, cavity detuning and cavity
quality-factors. The demonstrated system provides a prototype where atomic- and
photonic-scale orders strongly couple, opening opportunities of photonic
engineering of quantum materials and novel photonic devices, such as compact,
on-chip polarized light source and polariton laser