A robust Multimodal Large Language Model (MLLM) for Earth Observation should maintain consistent interpretation and reasoning under realistic input variations. However, current Remote Sensing MLLMs fail to meet this requirement. Trained on carefully curated clean datasets, they learn brittle mappings that do not generalize to noisy conditions in operational Earth Observation. Consequently, their performance degrades when confronted with imperfect inputs in deployment. To quantify this vulnerability, we construct a realistic set of multimodal perturbations, including visual degradations such as cloud and fog cover, together with diverse human-centric textual variations ranging from colloquialisms to vague or omitted instructions. Empirical evaluations show that these perturbations significantly impair the visual-semantic reasoning capabilities of leading RS foundation models. To address this limitation, we introduce RemoteShield, a robust Remote Sensing MLLM trained to maintain consistent outputs across realistic input variations. During training, each clean sample is paired with its image-text perturbed variants to form a semantic equivalence cluster. Rather than directly fitting noisy samples, RemoteShield is optimized through preference learning over clean and perturbed conditions within the same cluster. By comparing model responses to clean and corrupted inputs, the model is encouraged to favor stable responses over perturbation-induced failures. This cross-condition alignment helps the model focus on underlying task semantics despite visual degradations and textual noise. Experiments on three Earth Observation tasks show that RemoteShield consistently delivers stronger robustness and cross-condition consistency than representative baselines under realistic multimodal perturbations.