Which is why most popular sci-fi franchises end up with velocity caps, justified either in-universe or out-of-universe. E.g. Star Trek sublight propulsion (impulse engine) has been established indirectly and through "word of God" to work with speeds up to ~1/3 c, which is not enough for relativistic effects to cause a big impact. The issue is conveniently omitted, because why travel fast through "normal space" when you have easy access to warp drive / jump drive / hyperdrive / wormholes, that gives you FTL and happens to drop you out into a convenient reference frame? And all the interesting action happens around planets anyway.

This omission makes it easy for the writers to introduce relativity as a nerdy plot point. For example, StarGate: Atlantis had an episode with a ship traveling absurdly close to the speed of light, which was devised as a convenient way to introduce characters that should've been dead for many thousands of years.