We introduce non-Hermitian plasmonic waveguide-cavity structures based on the Aubry-Andre-Harper model to realize switching between right and left topological edge states (TESs) using the phase-change material Ge2Sb2Te5 (GST). We show that switching between the crystalline and amorphous phases of GST leads to a shift of the dispersion relation of the optimized structure so that a right TES for the crystalline phase, and a left TES for the amorphous phase occur at the same frequency. Thus, we realize switching between right and left TESs at that frequency by switching between the crystalline and amorphous phases of GST. Our results could be potentially important for developing compact reconfigurable topological photonic devices.