The laws of physics, as described by the theory of relativity, are indeed consistent and applicable in all inertial reference frames. This is a fundamental principle of relativity known as the principle of relativity or the principle of covariance.
When we say that the laws of physics are the same in all inertial reference frames, we mean that the fundamental equations and principles remain unchanged when we transition from one inertial frame to another through a process called a Lorentz transformation. These transformations involve adjustments to quantities like time, length, and energy to account for the effects of time dilation and length contraction.
The so-called "fundamental constants" of nature, such as the speed of light (c) or the Planck constant (h), do indeed have units that depend on the choice of units for time, length, and mass. However, the numerical values of these constants are independent of the choice of units. In other words, the values of these constants are the same in all inertial reference frames.
The principles of relativity require that the laws of physics are expressed in a way that is consistent with the observed invariance of these fundamental constants. For example, in the theory of special relativity, the laws of electromagnetism are expressed in terms of the speed of light, which is a constant that does not change with the motion of the observer. This allows the laws of electromagnetism to be consistent in all inertial reference frames.
In summary, while the units of fundamental constants depend on the choice of units for time, length, and mass, the numerical values of these constants remain invariant. The laws of physics are formulated in a way that maintains this invariance and ensures consistency across all inertial reference frames.