And yet it was never abandoned. In SR the speed of light is invariant in inertial reference frames, but the coordinate speed of light can vary -- even wildly -- in non-inertial coordinate systems. Simple examples of this are the coordinate speed of light in accelerating and rotating reference frames. The invariance of
c postulate holds in GR in exactly the same sense and with the same limitations and caveats as it does in SR. Nothing has changed between SR and GR as far as the speed of light is concerned. The only thing that
has changed is that SR assumes the existence of globally inertial reference frames (i.e. flat spacetime) while GR relaxes this requirement (i.e. allows curved spacetime).
In fact, take that GIF you keep posting, which depicts a vaying coordinate speed of light between two light clocks at different altitudes near the Earth's surface. How do you think that's actually derived? Most of the variation depicted simply comes from working out how the coordinate speed of light varies in an accelerating reference frame
according to SR, and then applying the equivalence principle. The situation
would not look that way for a free-fall observer for instance, and it could even be
inverted for an observer accelerating downward.
This is where you run into a problem if you try to treat the coordinate speed of light as a physical quantity and try to relate it to some idea of spatial inhomogeneity: the coordinate speed of light can vary or not vary depending on trifles like how you define coordinates or whether you're accelerating or not.
Suppose you're in a rocket in nearly empty space far away from any gravitating mass, such that the gravitational field is negligible. You do some experiments with light pulses and light clocks and find that the speed of light is invariant, just as SR says it should be. You then turn the rocket engine on and start accelerating. You repeat all your experiments and find that now, the coordinate speed of light is no longer constant, again just like SR says it should be. You furthermore find that the path light takes can bend, as depicted
here for instance.
How do you explain that? Did all the space around you suddenly become inhomogeneous just because you started accelerating? Can the same region of space be homogeneous for one observer and inhomogeneous for another?