It is as firm as our understanding of gravity. There is still plenty left to learn about gravity, but if I throw a ball into the air I'm pretty damned certain it will fall back to the ground. The fundamentality of c as a limit of information propagation is one of those properties that has shown itself to be true so often that anything showing it false is considered a mistake until we can prove otherwise. Conservation laws are similar.
Sure, any reasonable scientist would tell you that there is a non-zero chance that we're wrong about these things and both perpetual motion and FTL are actually possible, it's just that we have an extremely high confidence they're not.