When the medium behaves as a linear system, superposition is valid. When you add a DC signal to an AC signal, you still can recover the AC signal. The same is valid for light (AC signal) and a DC magnetic field (DC signal). In this case magnetic fields do not interfere with the propagation of the light wave.
It goes wrong (for example) when charge is moved by the light wave. This results in movement of the charge (depending on qcharge/mcharge ratio). That moving/oscillating charge (with same frequency as the light) does emit light itself. This light interferes with the incident light wave. Moving charge in a magnetic field is subjected to a sideways acting force. This causes the direction of the moving charge to deviate from the direction of the E-field component of the light. So the polarization can change and this is known as Faraday rotation.
The same happens in the ionosphere where radio waves in the HF region (say up to about 30 MHz) are bended back towards earth enabling long distance communication without satellites. Besides bending towards earth, polarization changes and a second (extra-ordinary) wave front appears due to what is called birefringence. It is the earth magnetic field that causes the strange polarization effects.
You may try a search on magneto optical switch