If you write the magnetic field as a superposition of DC and AC, and take the curl to form Maxwell's equations, the contribution at DC essentially vanishes. Then write the mating Maxwell equation (Faraday's law) to obtain wave propagation in free space unaffected by the presence of the magnet.
The Faraday effect is a problematic example here, since the DC and AC fields are polarized orthogonal to each other. In fact, the Faraday effect occurs in gyroptropic media, which, when polarized, respond differently to AC fields of opposite circular polarization, provided that the polarizing DC field points perpendicular to the plane containing the AC magnetic vectors.
Magnetic resonance provides an interesting example: spins polarized in a DC field, and irradiated with an AC field polarized perpendicular to that DC field, will absorb a photon from one circular polarization or the other, but not both -- depending on the sign of the gyromagnetic ratio.