  We investigate the impact of site dilution by setting the on-site repulsion
strength ($U$) to zero at a fraction of sites in the half-filled Hubbard model
on a simple cubic lattice. We employ a semi-classical Monte-Carlo approach
first to recover the zero dilution (undiluted $x=1$) properties, including $U$
dependence of insulator to metal crossover temperature scale $T^*$ and
long-range staggered antiferromagnetic ordering temperature ($T_N$). For the
non-perturbative regime of $U \sim$ bandwidth, we find a rapid suppression of
$T^*$ with reducing $x$ from 1 to 0.7. However, $T_N$ remains unchanged in this
dilution range, showing a weakening of the insulating state but not of the
magnetic order. At $x \leq 0.7$, $T^*$ and $T_N$ coincide and are suppressed
together with further increase in site-dilution. Finally, the system loses the
magnetic order and the insulating state for $x=0.15$, significantly below the
classical percolation threshold $x_p^{sc} (\sim 0.31$). We show that the
induced moments on $U=0$ sites drive the magnetic order below the classical
percolation limit by studying local moment systematics and finite-size analysis
of magnetic order. At the end, we show that either increasing $U$ to large
values or raising temperature beyond a $U$ dependent critical value, suppresses
the induced local moments of the $U=0$ sites and recovers the classical
percolation threshold.
