Summary: We show that the non CM part of \(\ell\)-adic étale cohomology of any compact quaternionic Shimura variety with coefficients in any automorphic local system is a semisimple Galois representation. If the local system has weight \(k = (k_1,\ldots,k_d)\) with all \(k_i\) of the same parity, the full \(\ell\)-adic étale cohomology is semisimple. For Hilbert modular varieties, analogous results are proved for \(\ell\)-adic intersection cohomology of the Baily-Borel compactification. The proof combines a representation-theoretical criterion of semisimplicity with Eichler-Shimura relations for partial Frobenius morphisms.