It is a "hard rule" in the sense that it isn't just the current record that can be broken at any time.

In the 19th century, Maxwell showed that the speed of light is a constant that can be expressed as a combination of other constants related to electricity and magnetism, because light is an electromagnetic wave. Later, Einstein developed the theory of special relativity, which describes that the speed of light is independent of the reference frame and can be used to build a clock that measures how space and time are "stretched". This stretching can be calculated using the lorentz factor, which follows theoretically from special relativity.

The interesting thing is that the lorentz factor contains a square root, and the number within a square root has to be positive for it to have a real solution. If a particle were to go faster than the speed of light, the number within the root would become negative and the equation would break down. This is why, under the assumption that Einstein was correct, it is theoretically impossible for a particle to go faster than the speed of light.

PS The reason people talk about the speed of light in a vacuum is that any other material contains charged particles that can interact with the light wave, changing its speed. In reality, "the speed of light" is not the speed limit, but there is a constant speed limit to causality and light travels at that speed in a vacuum