A charged black hole is not the same as a black hole with charge. The Reissner-Nordström metric has the shape (see https://de.wikipedia.org/wiki/Reissner-Nordstr%C3%B6m-Metrik):
\begin{equation}
\mathrm{d}s^2 = -\left(1-\frac{2GM}{c^2 r} + \frac{Q^{2} K G}{ c^4 r^2}\right)c^2 \mathrm{d}t^2 +\left(1-\frac{2GM}{c^2 r} + \frac{Q^{2} K G}{ c^4 r^2}\right)^{-1} \mathrm{d}r^2 + r^2(\sin^2\theta\,\mathrm{d}\phi^2+\mathrm{d}\theta^2).
\end{equation}
Pleasse note that charge enters metric quadratic. It could be therefore concluded that gravitation makes no difference between charge signs. In my understanding, a black hole has no electric charge, or is electric charged.