In non-diffusive conduction regimes of strongly correlated quantum electron systems, electromagnetic perturbations simultaneously probe the electronic dynamics in time and space: the exchanged energy $\hslash \omega$ excites retarded, i.e., frequency-dependent, many-body interactions, while the probing spatial modulation renders the response spatially nonlocal, i.e., dependent on the external wave vector $\vec{q}$. This work derives the nonlocal electrodynamic response of such dynamical quantum fluids under the assumptions of local but frequency-dependent self-energies, local but frequency-dependent particle-hole irreducible two-particle vertex functions, and charge/mass conservation. The latter is ensured by Bethe-Salpeter equations for renormalized interaction vertices, entering the Kubo formalism for two-particle correlation functions (e.g., for density, currents, momentum, stress). Within such a framework, exact symmetry criteria for the presence or absence of vertex corrections are inferred. In particular, it is shown that vertex corrections generally vanish at $q=0$ for single-particle dispersions that are even and bare interaction vertices that are odd with respect to specific point group transformations in momentum space, including inversion for vector vertices, and mirror reflections or two- or higher-fold rotations for tensor vertices. If the dispersion is isotropic, then the transverse part (orthogonal to $\vec{q}$) of vectorial vertices (such as for electric/particle current, momentum, and energy current) is devoid of vertex corrections at any finite $\hslash \omega$ and $\vec{q}$. Moreover, for quadratic and isotropic dispersion the full current-current correlation function can be computed with the bare (unrenormalized) current vertex, at any momentum $\vec{q}$ and frequency $\omega$, and still preserving charge conservation. The robustness of these criteria against further symmetry breaking, multiband effects, and additionally imposing momentum conservation, is discussed, with application to the Hall viscosity of Landau levels. Explicit expressions for generic nonlocal correlation functions are derived for Fermi liquids (with well-defined quasiparticle peaks) and non-Fermi liquids (devoid of quasiparticles), for arbitrary local self-energies.