Let $(E,\phi)$ be a $G$-Higgs bundle $\phi\in H^{0}(X,ad(E)\otimes D)$ where $D$ is a divisor on X.

I suppose that $(E,\phi)\in \mathcal{M}^{ani}$ the anisotropic locus.

In particuler, this bundle is stable as a Higgs bundle because, it doesn't have any reduction to a parabolic.

Does it imply that the underlying bundle $E$ is itself stable?

More generally, when a stable Higgs bundle has a stable underlying bundle.