Legal reasoning requires distinguishing changes that matter from those that do not. Legal AI should remain stable under legally irrelevant perturbations, but should change when perturbations alter legally material points. We formulate this requirement as a legal-relevance-sensitive evaluation problem: LLMs should only be sensitive to the legally relevant change. We introduce a unified evaluation suite covering should-change and should-not-change evaluation across judicial fairness, robustness, and statute-confusion scenarios. Our evaluation shows that existing legal LLMs are systematically sensitive to legally irrelevant variations and often fail to distinguish related legal elements and statutory rules. To mitigate these failures, we present LexGuard, an adversarial multi-agent framework grounded in formal reasoning. LexGuard formalizes statutes into executable constraints, uses adversarial agents to extract competing fact-statute arguments, and invokes SMT solvers to verify legal satisfaction and logical consistency. Experiments show that LexGuard improves legal reasoning reliability by reducing vulnerability to manipulative framing, improving disambiguation among similar statutes, limiting the influence of legally irrelevant attributes, and increasing consistency under benign reformulations. We show that legal trustworthiness requires not only accuracy, but calibrated sensitivity to legally material changes.