So what you are saying is that if we assumed that all particles, including light are magnetic, and everything that has a mass, emits a corresponding magnetic field with a strength relative to its mass, we could not form a similar theory of "general magnetic relativity" in which the frame of reference under magnetic fields would behave in a similar way it does for gravity?

That seems kinda odd. What exactly would provide this difference? How is magnetism different from gravity? Is it that gravity doesn't have a mass, but magnetic fields do?