High-brilliance synchrotron radiation sources have opened new avenues for x-ray polarization analysis that go far beyond conventional polarimetry in the optical domain. With linear x-ray polarizers in a crossed setting, polarization extinction ratios down to 10 − 10 can be achieved. This renders the method sensitive to probe the tiniest optical anisotropies that would occur, for example, in strong-field quantum electrodynamics due to vacuum birefringence and dichroism. Here we show that high-purity polarimetry can be employed to reveal electronic anisotropies in condensed matter systems with utmost sensitivity and spectral resolution. Taking CuO and L a 2 C u O 4 as benchmark systems, we present a full characterization of the polarization changes across the Cu K-absorption edge and their separation into dichroic and birefringent contributions. At diffraction-limited synchrotron radiation sources and x-ray lasers, where polarization extinction ratios of 10 − 12 can be achieved, our method has the potential to assess birefringence and dichroism of the quantum vacuum in extreme electromagnetic fields.