Control over isospin-breaking corrections is an important prerequisite for the evaluation of hadronic contributions to the anomalous magnetic moment of the muon, both regarding the isospin rotation of hadronic $\tau$ decays and the comparison of data-driven evaluations of hadronic vacuum polarization with lattice QCD. In both cases, a key point concerns the definition of the isospin scheme. Here we discuss recent work aimed at improving these corrections as well as the required matching procedure.