We develop an effective medium theory for electromagnetic wave propagation through gapless nonuniform systems with a dynamic chiral magnetic effect. The theory allows us to calculate macroscopic-disorder-induced corrections to the values of optical, as well as chiral magnetic conductivities. In particular, we show that spatial fluctuations of the optical conductivity induce corrections to the effective value of the chiral magnetic conductivity. The absolute value of the effect varies strongly depending on the system parameters, but yields the leading frequency dependence of the polarization rotation and circular dichroism signals. Experimentally, these corrections can be observed as features in the Faraday rotation angle near frequencies that correspond to the bulk plasmon resonances of a material. Such features are not expected to be present in single-crystal samples.