  Using the Seiberg-Witten monopole equations, Baraglia recently proved that
for most of simply-connected closed smooth $4$-manifolds $X$, the inclusions
$\mathrm{Diff}(X) \hookrightarrow \mathrm{Homeo}(X)$ are not weak homotopy
equivalences. In this paper, we generalize Baraglia's result using the
$\mathrm{Pin}^{-}(2)$-monopole equations instead. We also give new examples of
$4$-manifolds $X$ for which $\pi_{0}(\mathrm{Diff}(X)) \to
\pi_{0}(\mathrm{Homeo}(X))$ are not surjections.
