> I often worry whether the EE degree disqualifies me in the eyes of employers from being a "serious" programmer.
If it does then that employer doesn't know what a "serious" programmer is, regardless what they say on their job spec. A serious programmer is one who knows the entire tech stack, from how the electrons move around in circuits, to high level mathematical computer science, and everything in between, and uses all of that knowledge to design and build more efficient, performant, correct, and secure systems.