$E = mc^2$ tells us that energy and matter are interchangeable, and this lines up with quantum field theory. If that's the case, would that mean that matter is a low entropy form of energy? And to extrapolate on that, doesn't that mean the universe will progress to a state where all matter will be liberated to form high entropy energy?
You are confusing "matter" with "mass". Specifically, $m$ in $E=mc^2$ is not "matter", but mass. "Matter" is a more general term. Both mass and energy are matter. Strictly speaking, mass is the inertia of energy, usually of the energy that is localized. 99% of mass of the ordinary matter is the energy of gluons that move with the speed of light inside neutrons and protons in the nucleus of atoms of the elements, of which everything is made. The remaining 1% comes from the energy of interactions with the Higgs field, electromagnetic energy, and a number of other types of energy.
To better understand the concept of entropy, this Wikipedia article may be a good start.