Opto-mechanical interactions in guided wave media are drawing great interest in fundamental research and applications. Forward stimulated Brillouin scattering, in particular, is widely investigated in optical fibres and photonic integrated circuits. In this work, we report a comprehensive study of forward stimulated Brillouin scattering over standard, panda-type polarization maintaining fibres. We distinguish between intra-polarization scattering, in which two pump tones are co-polarized along one principal axis, and inter-polarization processes driven by orthogonally polarized pump waves. Both processes are quantified in analysis, calculations and experiment. Inter-modal scattering, in particular, introduces cross-polarization switching of probe waves that is non-reciprocal. Switching takes place in multiple wavelength windows. The results provide a first demonstration of opto-mechanical non-reciprocity of forward scatter in standard fibre. The inter-polarization process is applicable to distributed sensors of media outside the cladding and coating boundaries, where light cannot reach. The process may be scaled towards forward Brillouin lasers, optical isolators and circulators and narrowband microwave-photonic filters over longer sections of off-the-shelf polarization maintaining fibres.