Thyroid disorders affect millions globally, underscoring the urgent need for accurate and reliable diagnostic tools. Conventional diagnostic methods are often time-consuming, invasive, and prone to inconclusive results, whereas existing machine learning (ML) approaches continue to face persistent challenges with outliers, data imbalance, interpretability, and generalization. To address these challenges, this study proposes a robust meta-learning framework that integrates hybrid outlier handling, feature selection, Bayesian hyperparameter optimization, and explainable artificial intelligence (XAI) for binary classification of thyroid disease. This study introduces a hybrid outlier-handling framework combining univariate Interquartile Range (IQR) analysis, multivariate Isolation Forest detection, and regression-based contextual imputation. Class imbalance was mitigated using Random Oversampling (ROS), and key predictive features were identified using a Recursive Feature Elimination (RFE). The selected features were used to train Random Forest and XGBoost, which were subsequently combined in a stacking ensemble with a logistic regression meta-learner. The proposed framework demonstrated state-of-the-art performance, achieving an accuracy of 99.74%, an Area Under the Receiver Operating Characteristic Curve (AUC-ROC) of 0.9994, and a Cohen's Kappa score of 0.9769. Stratified 10-fold cross-validation confirmed its stability with an average accuracy of 99.70%, highlighting strong generalization. Robustness tests under adversarial perturbations (ε = 0.01, 0.05, 0.1) and Gaussian noise demonstrated minimal performance degradation, with accuracies consistently above 96%. Model transparency is achieved using SHapley Additive exPlanations (SHAP) and Local Interpretable Model-agnostic Explanations (LIME), which provide global and local explanations of feature contributions. Overall, the proposed framework demonstrates high accuracy, robustness, and transparency, supporting its suitability for real-world AI-assisted thyroid disease diagnosis.