For one thing, there is no such fundamental principle. In relativity (both special and general), there is a speed, c, that’s the same to all observers—meaning that no matter how fast different observers are moving, they all agree on its value. That speed happens to be the speed massless particles naturally move at, so if light is massless (as current best measurements show), then c is the speed of light.
But there’s, despite some unclear presentations of the subject, no actual prohibition to traveling faster than that speed—there are solutions of the theory that describe faster-moving objects (tachyons). However, what you can’t do is take something that’s moving slower than light, and accelerate it beyond c, as that would need infinite energy—so in that sense, it’s the fastest speed you can attain. (And also, once you include quantum physics into the mix, tachyons become problematic, because they end up destabilizing the vacuum, which would be bad.)
However, there may be ways to go around this minor engineering issue. For one, general relativity has wormhole solutions, and wormholes, if they are traversable, would allow going between their openings faster than a ray of light could traverse the distance without ‘going through’. But there’s also the possibility of ‘warp drives’—basically, generating a superluminally moving ‘bubble’ by contracting and expanding space in front of and behind the ‘spacecraft’.
A problem with this is that while it’s a solution of general relativity, it’s only a ‘solution’ in the sense that you can write down a spacetime deformed in the right way, and from that, generate a matter distribution that would lead to such a spacetime—but that matter distribution doesn’t end up making a whole lot of sense, containing things like ‘negative energy’ etc. But there’s been some recent buzz around a paper soon to be published that might make this sort of thing a little more plausible.
So, to answer the question in the OP: it’s hard science fiction if the above is taken into account, and at least some plausible story exists to justify the fictional conceit. So one might posit that the new paper actually leads to the creation of a feasible warp drive—which it probably won’t—and then explore the effects of that in a consistent way. ‘Soft’ science fiction, on the other hand, just goes with the ‘finger-snapping’ approach, and uses technology as a means to advance plots—if you need something to get you from A to B faster than a ray of light, you just conjure something up. That is, to me, the most succinct distinction: scientific plausibility is a constraint on hard SF-stories, while technological miracles are just a means to an end in soft SF.