EEG-based neural decoding models often fail to generalize across acquisition sites due to structured, site-dependent biases implicitly exploited during training. We reformulate cross-site clinical EEG learning as a bias-factorized generalization problem, in which domain shifts arise from multiple interacting sources. We identify three fundamental bias factors and propose a general training framework that mitigates their influence through data standardization and representation-level constraints. We construct a standardized multi-site EEG benchmark for Major Depressive Disorder and introduce CRCC, a two-stage training paradigm combining encoder-decoder pretraining with joint fine-tuning via cross-subject/site contrastive learning and site-adversarial optimization. CRCC consistently outperforms state-of-the-art baselines and achieves a 10.7 percentage-point improvement in balanced accuracy under strict zero-shot site transfer, demonstrating robust generalization to unseen environments.