Modern ASR systems are increasingly deployed in high-stakes settings, including clinical interviews, public services, and educational tools, where equitable performance across speaker groups is essential. While pre-trained models like Whisper achieve strong overall accuracy, they often exhibit inconsistent group-level performance that varies across domains. These disparities are not fixed properties of the model, but emerge from the interaction between model, data, and task—posing challenges for fairness interventions designed in-domain. We frame fairness in ASR as a generalisation problem. We fine-tune Whisper on a diverse corpus using four strategies: standard fine-tuning, demographic rebalancing, gender-swapped data augmentation, and a novel contrastive learning objective that encourages gender-invariant representations. We evaluate performance across multiple aspects of fairness and utility, both in-domain and on three out-of-domain test sets: LibriSpeech, EdAcc, and CognoSpeak. Our findings show that the method with the best in-domain fairness performed worst out-of-domain, illustrating that fairness gains do not always generalise. Demographic balancing generalises more consistently, while our contrastive method offers a practical alternative: it achieves stable, cross-domain fairness improvements without requiring changes to the training data distribution, and with minimal accuracy trade-offs.