Ensuring fairness in natural language processing for moral sentiment classification is challenging, particularly under cross-domain shifts where transformer models are increasingly deployed. Using the Moral Foundations Twitter Corpus (MFTC) and Moral Foundations Reddit Corpus (MFRC), this work evaluates BERT and DistilBERT in a multi-label setting with in-domain and cross-domain protocols. Aggregate performance can mask disparities: we observe pronounced asymmetry in transfer, with Twitter->Reddit degrading micro-F1 by 14.9% versus only 1.5% for Reddit->Twitter. Per-label analysis reveals fairness violations hidden by overall scores; notably, the authority label exhibits Demographic Parity Differences of 0.22-0.23 and Equalized Odds Differences of 0.40-0.41. To address this gap, we introduce the Moral Fairness Consistency (MFC) metric, which quantifies the cross-domain stability of moral foundation detection. MFC shows strong empirical validity, achieving a perfect negative correlation with Demographic Parity Difference (rho = -1.000, p < 0.001) while remaining independent of standard performance metrics. Across labels, loyalty demonstrates the highest consistency (MFC = 0.96) and authority the lowest (MFC = 0.78). These findings establish MFC as a complementary, diagnosis-oriented metric for fairness-aware evaluation of moral reasoning models, enabling more reliable deployment across heterogeneous linguistic contexts. .