I mean, before Einstein's version of relativity, folks were perfectly happy doing Newtonian relativity where the speed of light can change, and they felled a lot of trees writing papers explaining how such a system could work!
That predates Maxwell, right? My vague recollection was that one of the motivations for Lorentz invariance was that Maxwell’s equations already satisfied it.
Yes and no! Maxwell's equations are Lorentz invariant, but folks spent a good many years trying to fit them into Newtonian relativity instead, which is what caused all sorts of complicated strange math.
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https://physics.stackexchange.com/a/373643/227698