How DNA sequence encodes gene regulation remains a central challenge in regulatory genomics. Transcription factors (TFs) are key mediators of this process, binding to specific sequence motifs to control gene expression. Yet, predicting where they bind from sequence alone remains a challenging problem. A cross-species angle offers two complementary benefits: it tests whether trained models have learned conserved, biochemically grounded rules that generalize across species, and it enables binding prediction in species where experimental data is scarce. Key challenges in this context are that TF binding sites undergo rapid evolutionary turnover, and that there are systematic distributional differences between species’ genomes. We present MORALE, a domain adaptation framework for cross-species TF binding prediction. By aligning the first and second moments of sequence embeddings across species during training, MORALE learns species-invariant representations without adversarial training, additional parameters, or architectural changes. Applied to liver ChIP-seq data from two species (human, mouse) and five species (adding rhesus macaque, rat, and dog), MORALE consistently matches or outperforms gradient reversal (the adversarial baseline) across all TFs, and avoids the performance degradation below the no-adaptation baseline that gradient reversal can exhibit. In the five-species setting, MORALE surpasses a human-only model, demonstrating that moment alignment can unlock cross-species generalization that neither multi-species training nor adversarial adaptation achieves alone. MORALE also recovers TF binding motifs more faithfully than the adversarial approach, suggesting its representations capture biologically meaningful sequence features. As a closed-form, parameter-free regularizer, MORALE integrates into any embedding-based sequence model.