We demonstrate a bio-inspired coating for novel imaging and sensing designs: the coating sorts different colors and linear polarizations. This coating, composed of conducting, nanofibrous polyaniline in an inverse opal film (PANI-IOF), is inexpensive and can feasibly be deposited over large areas on a range of flexible and non-flat substrates. With PANI IOFs, light is scattered into azimuthally polarized Debye rings. Subsequently, the diffracted speckle patterns carry compressed representations of the polarized illumination, which we reconstruct using shallow neural networks.