In other words Newtonian physics are an accurate enough approximation to the more precise theory, special relativity. ... Other than that some conservation laws from Newtonian physics carry on to the rest of physics, for example conservation of energy and momentum.

Is Newtonian physics still valid?

Even though three centuries have passed since Isaac Newton published his theory of gravitation in 1687, scientists are still testing it. ... They found that Newton's law was still valid even at this distance.

Are Newtonian mechanics false?

For applications of mechanics at low speeds, Newtonian ideas are almost equal to reality. That is the reason we use Newtonian mechanics in practice at low speeds. On a conceptual level, Einstein did prove Newtonian ideas quite wrong in some cases, e.g. the relativity of simultaneity.