I'm not an expert either, but I like to think that the speed of causality is the speed at which a piece of information (e.g. a particle, a gravity wave, etc) is traveling through space.
So the speed of light / gravity is essentially the maximum speed of causality, because nothing can travel faster than that.
EDIT: Or you can think in terms of how information propagates through spacetime. In this point of view, the speed of causality is always the speed of light, for everything, including particles with mass.
Yeah that's what I was trying to work towards. Basically that causality is an abstraction, or at least a "higher level" idea. And if we look at the components of it, we can see that interaction between two things is a central part of it. And an interaction between two things in our universe has a maximum bound of the speed of light (and gravity and so on). The speed of causality is just the speed of the fastest thing.
It's the reverse. Light and gravity travel at c because they (at least light) are mediated by particles / systems that have no mass.
Mass is what slows the speed of causality for certain particles. For example, while the photons I emit may travel at C, the massive particles that make up 'me' cannot.
So the speed of light / gravity is essentially the maximum speed of causality, because nothing can travel faster than that.
EDIT: Or you can think in terms of how information propagates through spacetime. In this point of view, the speed of causality is always the speed of light, for everything, including particles with mass.