Malus first discovered light polarization just before 1810, but Maxwell's equation stuff came around 1860s. How was polarization interpreted before the EM theory?
Short version: they either considered a wave in the aether (the aether being some mysterious medium that filled space allowing for only transverse waves) or corpuscules with additional degrees of freedom.
Along with his discovery, Malus tried to explain polarization of light using the "particle theory". He just stated that light corpuscules could have an alignment similar to that of a bar magnet in a magnetic field.
Based on 1816 polarization experiments of Arago and Fresnel, Thomas Young (who considered a "wave theory" of light) deduced in 1817 that light have to be a transverse wave. Fresnel would later write his theory of light (1832) propagation founded on the idea that light is a transverse wave on the aether.
One had to wait until Maxwell (even if some others already hinted at it) to tie light to electromagnetism through Maxwell's equations.
With Michelson–Morley experiment (1887) and later with the success of Einstein's special relativity (1905) the idea of aether would be put in the coffin. EM waves can travel without medium.
Note that if light was a wave or a particle it does not matter anymore, with quantum mechanics we have understood that is something more complex.
The idea of luminiferous aether appears a bit earlier, Huygens already discussed the idea in 1690 Traité de la Lumière: but he was not carrying polarization experiments. The corpuscular theory of light goes back to Newton's Opticks (1704).