They will be called “variables” in the future, and scientists will try to figure out how they tick. And: They were seen as constants for a sufficientyl long time, so still treating them like constants won’t hurt, as the value will probably only vary over long reaches of time or unlikely/uncommon circumstances like relativistic speeds.

We treat g = 9.81m/s², well knowing that this changes depending on height and location. But this value is totally sufficient for everyday purposes, and no bridge will ever collapse just because of local derivations from 9.81. The precise local value of g is only of relevance for a very small range of applications.

I imagine a few physicists will be a little upset.

In math context, we’d just call it variable and move on.

It won’t affect much except bleeding edge theoretical physics. Much the way we don’t need relativity to make airplanes fly (but round-earth gravity models help for long distance flights).

Physical laws are mathematical models that reflect natural forces and predict outcomes (accurately that we can fling cans of passengers across the world safely). It wouldn’t be the first time we discovered that some previously constant forces are actually variable (much the way the force of gravity is affected by distance, noticeable only when you lob something high enough.) We shrug and change the variables, and some physicists near retirement may balk and say it’s ridiculous, as Einstein did regarding Heisenberg’s probability-based quantum mechanics.