  We investigate how magnetic impurities may affect a system exhibiting
charge-density wave (CDW) in its ground state. We consider a disordered
Hubbard-Holstein model with a homogeneous electron-phonon interaction, but with
a (randomly chosen) fraction of sites displaying a non-zero Coulomb repulsion,
$U$, and perform state-of-the-art finite-temperature quantum Monte Carlo
simulations. For a single magnetic impurity, charge-charge correlations hamper
the spin-spin ones around the repulsive site, thus requiring a strong enough
value of $U$ to create non-negligible antiferromagnetic (AFM) correlations. As
the number of magnetic impurities increases, these AFM correlations become
deleterious to CDW order and its features. First, the critical temperature is
drastically reduced, and seems to vanish around 40$\%$ of impurities (for fixed
$U/\lambda=2$), which we correlate with the classical percolation threshold. We
also notice that just a small amount of disorder suffices to create a
\textit{bad insulating} state, with the suppression of both Peierls and spin
gaps, even within the charge-ordered phase. Finally, we have also found that
pairing correlations are enhanced at large doping, driven by the competition
between CDW and AFM tendencies.
