Considering inflationary magnetogenesis induced by time-dependent kinetic and axial couplings of a massless Abelian vector boson field breaking the conformal invariance, we show in this article that, surprisingly, the spectral shape of the large-scale primordial magnetic field power spectrum is insensitive to the postinflationary history, namely, the barotropic parameter (w) and the gauge coupling functions of the postinflationary era.