At thermal equilibrium, we find that generalized susceptibilities encoding the static physical response properties of Hermitian many-electron systems possess inherent non-Hermitian (NH) matrix symmetries. This leads to the generic occurrence of exceptional points (EPs), i.e., NH spectral degeneracies, in the generalized susceptibilities of prototypical Fermi-Hubbard models, as a function of a single parameter such as chemical potential. We demonstrate that these EPs are necessary to promote correlation-induced thermodynamic instabilities, such as phase separation occurring in the proximity of a Mott transition, to a topologically stable phenomenon.