Vision-language models (VLMs) are increasingly used as automated judges for multimodal and embodied tasks, yet aggregate accuracy or consistency alone does not reveal whether a judge changes its verdict for the right reason. We propose State-Conditional Invariance (SCI), a reliability principle requiring a judge to remain stable under semantics-preserving changes in presentation while responding to causal interventions that change the task outcome. We instantiate SCI in GridWM-Judge, a simulator-grounded diagnostic benchmark built from deterministic MiniGrid trajectories with aligned Full, evidence-removal, and counterfactual variants, plus presentation and representation probes. Across five diagnostic tasks, GridWM-Judge tests local perception, action-conditioned transitions, presentation stability, representation exchangeability, and Full-CF causal discrimination. Our diagnostic evaluations reveal heterogeneous failure modes, including sensitivity to evidence presentation and encoding, low activation on successful trajectories, and weak paired counterfactual discrimination. Perception-controlled analyses further indicate that visual grounding and objective recovery are substantial, model-dependent bottlenecks. These results motivate jointly reporting correctness, presentation stability, and causal sensitivity instead of relying on a single score.