  For each classical irreducible bounded symmetric domain $\mathcal{D}$,
Klingler has computed the minimum number $m_{\mathcal{D}}$ such that any smooth
projective quotient $X=\mathcal{D}/\Gamma$, for
$\Gamma\in\textrm{Aut}^0(\mathcal{D})$, satisfies
$H^0(X,\mathrm{Sym}^i\Omega^1_X)=0$ for $0<i<m_{\mathcal{D}}$. In this article,
we extend Klingler's result to the case when $X$ is normal and projective.
This, together with a normal version of Arapura's result about the relationship
between the vanishing of global symmetric differentials on $X$ and the rigidity
of finite dimensional representations of $\pi_1(X)$, gives rigidity statements
for representations of $\pi_1(X)$ and $\pi_1(X_{reg})$ in a low dimensional
range, when $X$ is a normal projective quotient of a bounded symmetric domain.
