Vision-Language-Action (VLA) policies fuse multimodal sensory inputs, but training on limited and homogeneous robot demonstrations encourages spurious inter-sensor correlations rather than task-relevant signal, a failure we term modality entanglement. Under real-world occlusions and distractors, this manifests as nuisance sensitivity to corruption of uninformative sensors and single-modality insufficiency when only one informative sensor remains intact. We propose Evidence-Gated Regularization (EGR), a modality-agnostic training objective that introduces zero inference-time overhead. EGR derives a per-frame and per-sensor task-relevance signal to gate two state-conditional consistency objectives: invariance on low-evidence sensors, and single-sensor sufficiency on high-evidence ones. We introduce a benchmark based on BEHAVIOR-1K, comprising a fast inference-only diagnostic suite and 47 rollout-based skills targeting modality entanglement. We validate EGR on this benchmark and on two real-robot setups with fundamentally different embodiments: a bi-manual setup with two Kinova arms and three RGB cameras, and a single-arm MELFA ASSISTA setup combining vision and GelSight tactile sensors. EGR improves simulation success rates (SR) from 12.5