Is the speed of light really a constant or is it infinitely variable?

Is the speed of light really a constant or is it infinitely variable? It can be slowed according to the refractive index of the medium it is travelling through therefore is it not also possible that it can travel faster through a vacuum than we can currently measure? I know it is approximately 300 000 km/s through a vacuum but what effect would it have on Einstein's theory of relativity if the speed of light were not a constant? Why does faster than light travel need to be impossible, if it is possible to communicate faster than light then it would be possible to travel faster than light without getting into paradoxes even if we are not yet aware of its mechanism. If light speed were fixed (which it is not due to refractive index) then a paradox would only exist temporarily until the traveller dropped below light speed. Using sound as an ogy an observer can see an event before they hear it, if they were blind and travelled faster than sound they would never be aware of the event until they slowed below the speed of sound at which point they would become aware of the event (uming there was still sufficient energy in the sound for it to be detected) the same would be true for the speed of light we just aren't aware of faster than light mechanisms yet. Should we rule out FTL travel / communications just because we don't yet understand it.