Neutrino scattering and absorption rates of relevance to supernovae and neutron star mergers are obtained from nuclear matter dynamical structure functions that encode many-body effects from nuclear mean fields and correlations. We employ nuclear interactions from chiral effective field theory to calculate the density, spin, isospin, and spin-isospin response functions of warm beta-equilibrium nuclear matter. We include corrections to the single-particle energies in the mean field approximation as well as vertex corrections resummed in the random phase approximation (RPA), including, for the first time, both direct and exchange diagrams. We find that correlations included through the RPA redistribute the strength of the response to higher energy for neutrino absorption and lower energy for antineutrino absorption. This tends to suppress the absorption rate of electron neutrinos across all relevant energy scales. In contrast, the inclusion of RPA correlations enhances the electron antineutrino absorption rate at low energy and supresses the rate at high energy. These effects are especially important at high-density and in the vicinity of the neutrino decoupling region. Implications for heavy element nucleosynthesis, electromagnetic signatures of compact object mergers, supernova dynamics, and neutrino detection from galactic supernovae are discussed briefly.