Non-Hermitian optical metasurfaces have recently attracted interest as a platform for controlling light in amplitude, phase, and polarization. Here we predict that breaking parity-time symmetry in honeycomblike active plasmonic metasurfaces can lead to nonunitary circular dichroism at oblique incidence. This extraordinary chiroptical response is achieved through band folding that enables coupling of incident light to spin-polarized flat bands surrounded by exceptional rings, formed at Dirac points of plasmonic lattice resonances. The reported spin polarization differs from previously reported chiral and pseudochiral phenomena in that it solely emerges from spatial distribution of gain and loss and at the same time it does not involve the inherent chirality of isolated exceptional points, but instead it can be considered as a non-Hermitian counterpart of spin polarization of K-point valleys. Our findings may become useful in designing and realizing novel polarization-controlling optical elements and spin-polarized exceptional ring lasers.