State-of-the-art stereo matching networks trained only on synthetic data often fail to generalize to more challenging real data domains. In this paper, we attempt to unfold an important factor that hinders the networks from generalizing across domains: through the lens of shortcut learning. We demonstrate that the learning of feature representations in stereo matching networks is heavily influenced by synthetic data artefacts (shortcut attributes). To mitigate this issue, we propose an Information-Theoretic Shortcut Avoidance~(ITSA) approach to automatically restrict shortcut-related information from being encoded into the feature representations. As a result, our proposed method learns robust and shortcut-invariant features by minimizing the sensitivity of latent features to input variations. To avoid the prohibitive computational cost of direct input sensitivity optimization, we propose an effective yet feasible algorithm to achieve robustness. We show that using this method, state-of-the-art stereo matching networks that are trained purely on synthetic data can effectively generalize to challenging and previously unseen real data scenarios. Importantly, the proposed method enhances the robustness of the synthetic trained networks to the point that they outperform their fine-tuned counterparts (on real data) for challenging out-of-domain stereo datasets.