I love wave theory, how waves share behaviour whether it’s water or light. Working in optics must be a fascinating occupation.
I don’t think refraction violates the Theory of Relativity. That electromagnetic radiation in a vacuum is the same for all observers is the point, not that it still doesn’t refract. This speed is taken as the constant - a universal constant, and the rest of relativity can be seen as flowing from this. IIRC, this was the insight that led to the development of the theory. If the speed of light (in a vacuum) is a universal constant for all inertial frames, then what must happen to space, time, mass..
In the real world that is simply not absolutely true because the universe is not a perfect vacuum.
How does Einstein's theory account, for example, for the read shift?