The linear stability of zero and finite width, arbitrarily compressible, and magnetized velocity shear layers with isotropic or anisotropic pressure is investigated. Such flows, modeled by the magnetohydrodynamic equations with generalized polytrope laws for the pressure parallel and perpendicular to the magnetic field, are relevant in various astrophysical, geophysical and space plasma configurations. The conditions for instability of shear layers of zero width are derived. For layers of finite width, shooting numerical schemes are employed to satisfy the Sommerfeld radiation conditions of outgoing, spatially damping modes in a frame comoving with the plasma flow. The resulting eigenvalues for the angular frequency and linear growth rate are mapped out for different regions of the wave number/Mach number space. For polytrope indices corresponding to the double adiabatic and magnetohydrodynamic equations, the results reduce to those obtained earlier using these models.