Generalizing beyond the training domain in image-based behavior cloning remains challenging. Existing methods address individual axes of generalization, workspace shifts, viewpoint changes, and cross-embodiment transfer, yet they are typically developed in isolation and often rely on complex pipelines. We introduce PALM (Perception Alignment for Local Manipulation), which leverages the invariance of local action distributions between out-of-distribution (OOD) and demonstrated domains to address these OOD shifts concurrently, without additional input modalities, model changes, or data collection. PALM modularizes the manipulation policy into coarse global components and a local policy for fine-grained actions. We reduce the discrepancy between in-domain and OOD inputs at the local policy level by enforcing local visual focus and consistent proprioceptive representation, allowing the policy to retrieve invariant local actions under OOD conditions. Experiments show that PALM limits OOD performance drops to 8% in simulation and 24% in the real world, compared to 45% and 77% for baselines.