The proton finding won’t impact most people’s daily lives. But if it proves correct, it means something fundamental is wrong in particle physics.
It’s possible the smaller proton means the Rydberg constant hasn’t been correctly measured. This value describes the way light gets emitted from various elements—a key component of spectroscopy, which is used, for instance, to tell which kinds of elements exist in galaxies and the vast interstellar gas-and-dust clouds called nebulae.
Or, if the Rydberg constant is correct, the smaller size of a proton could mean the equations in QED theory will fail to work.
Atomic spectroscopy measures transitions of the electrons between orbits in the atom, and does not depend on the details of structure of the proton.
That's ok. We'll just make up a new theory.
I do not think that the QED is wrong. The radius of the proton is not derived from first principles, it has to be measured experimentally as it is not clear what the “proton density” is. We have no description of the orbits of quarks.