  For a Shimura variety $(G, X)$ in the superrigid regime and neat level
subgroup $K_0$, we show that the canonical family of $\ell$-adic
representations associated to a number field point $y \in \mathrm{Sh}_{K_0}(G,
X)(F)$,
  \[
  \left\{ \rho_{y, \ell} \colon \mathrm{Gal}(\overline{\mathbb{Q}}/F) \to
G^{\mathrm{ad}}(\mathbb{Q}_{\ell}) \right\}_{\ell},
  \]
  form a compatible system of
$G^{\mathrm{ad}}(\mathbb{Q}_{\ell})$-representations: there is an integer
$N(y)$ such that for all $\ell$, $\rho_{y, \ell}$ is unramified away from $N(y)
\ell$, and for all $\ell \neq \ell'$ and $v \nmid N(y)\ell \ell'$, the
semisimple parts of the conjugacy classes of $\rho_{y, \ell}(\mathrm{Frob}_v)$
and $\rho_{y, \ell'}(\mathrm{Frob}_v)$ are ($\mathbb{Q}$-rational and) equal.
We deduce this from a stronger compatibility result for the canonical
$G(\mathbb{Q}_{\ell})$-valued local systems on connected Shimura varieties
inside $\mathrm{Sh}_{K_0}(G, X)$. Our theorems apply in particular to Shimura
varieties of non-abelian type and represent the first such
independence-of-$\ell$ results in non-abelian type.
