Bound states in the continuum (BICs) enable optical modes with ideally infinite radiative lifetimes despite lying within the radiation continuum. Radiation-matter interaction in periodically patterned planar waveguides embedding two-dimensional (2D) optically active excitations can be described quantum mechanically by diagonalizing a non-Hermitian operator, known as the Hopfield matrix, which can be generalized to incorporate independent photonic and excitonic losses into the polaritonic states. However, since 2D excitons undergo intrinsic wavevector-dependent radiative decay within the light cone, whether the Hopfield formalism can consistently account for this process while preserving polariton BICs has remained an open question. Here we show that a non-Hermitian Hopfield formalism incorporating excitonic radiative losses correctly captures the existence of genuine k=0 polariton BICs with diverging radiative lifetimes. The theory provides a unified microscopic framework for radiative excitons and polariton BICs, and an efficient predictive tool for designing photonic-crystal platforms coupled to quantum wells, transition-metal dichalcogenides, and other 2D excitonic materials.