So, the typical handwaving argument is that one can prove $Z_1=Z_2$ for every charged particle. It does explain that if we have a bare Lagrangian which gives a certain ratio of charges of different fundamental particles, such ratio will survive quantum corrections and persist for experimental renormalized value. However, the proton is a composite particle. So, I don't see how that kind of argument is relevant to explaining proton and electron having exactly opposite renormalized charge.
This kind of argument is also very relevant for V-A weak interaction of hadron effective theory. Here we see that the $g_V$ of hadrons is exactly the same as those for leptons(which I don't understand for the same reason), while $g_A$ seems to receive QCD correction since QCD breaks axial symmetry.
