  The change of physical conditions across the turbulent and magnetized
interstellar medium (ISM) induces a 3D spatial variation of the properties of
Galactic polarized emission. The observed signal results from the averaging of
different spectral energy distributions (SED) and polarization angles, along
and between lines of sight. As a consequence, the total Stokes parameters $Q$
and $U$ will have different distorted SEDs, so that the polarization angle
becomes frequency dependent. In the present work, we show how this phenomenon
similarly induces a different distorted SED for the three polarized angular
power spectra $EE$, $BB$ and $EB$, implying a variation of the $EE/BB$ ratio
with frequency. We demonstrate how the previously introduced spin-moment
formalism provides a natural framework to grasp these effects, allowing us to
derive analytical predictions for the spectral behaviors of the polarized
spectra, focusing here on the example of thermal dust polarized emission. After
a quantitative discussion based on a model combining emission from a filament
with its background, we further reveal that the spectral complexity implemented
in the dust models commonly used by the cosmic microwave background (CMB)
community produce such effects. This new understanding is crucial for CMB
component separation, in which an extreme accuracy is required in the modeling
of the dust signal to allow for the search of the primordial imprints of
inflation or cosmic birefringence. For the latter, as long as the dust $EB$
signal is not measured accurately, great caution is required about the
assumptions made to model its spectral behavior, as it may not simply follow
from the other dust angular power spectra.
