Extending my previous question Angular moment and EM wave, does it make sense to talk about the angular momentum of electromagnetic waves in an anisotropic medium? It is not obvious that the angular momentum is conserved in this case. However, if the anisotropy is introduced by the external magnetic field (eg, magnetized plasmas), the projection of the angular momentum of a wave packet on the direction of the magnetic field might be conserved.
As was pointed out in an answer to your previous question, the polarization of your beam can be thought of as the "spin" angular momentum being carried by it. Circularly polarized light carries angular momentum, linearly polarized light does not (not counting the "orbital" angular momentum carried by the spatial profile of the beam).
Viewed in this light, I would say that angular momentum is not conserved when light propagates through an arbitrary anisotropic medium. A simple example is a half-waveplate, a device which can convert right-hand circular polarized into left-circular. Waveplates are very simple -- they are just a small plate of anisotropic material, cut to a certain width and with their "fast axis" oriented at some set angle relative to the input polarization.
Summing up, the angular momentum of light propagating in an anisotropic medium is not necessarily conserved. The excess angular momentum is, presumably, taken up by the medium.