= Solution
The <Faddeev-Popov ghost fields> $c$ and $\bar c$ are spin-zero <Grassmann fields> in the <Adjoint representation> of $G$; their statistics are anticommuting, despite their scalar transformation under spacetime rotations. The <Nakanishi-Lautrup field> $h$ is an auxiliary commuting spin-zero field, also in the <Adjoint representation>. Thus
$$
\boxed{c,\bar c:\ (0,\ \text{Grassmann odd},\ \mathrm{ad}\,G),\qquad h:\ (0,\ \text{Grassmann even},\ \mathrm{ad}\,G).}
$$
These <Faddeev-Popov ghost fields> are not physical spin-zero fermion states; they represent the gauge-fixing Jacobian, so their scalar spin does not contradict the physical <Spin-statistics theorem>.
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