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Stain variation is a unique challenge associated with automated analysis of digital pathology. Numerous methods have been developed to improve the robustness of machine learning methods to stain variation, but comparative studies have demonstrated limited benefits to performance. Moreover, methods to handle stain variation were largely developed for H&E stained data, with evaluation generally limited to classification tasks. Here we propose Stain Consistency Learning, a novel framework combining stain-specific augmentation with a stain consistency loss function to learn stain colour invariant features. We perform the first, extensive comparison of methods to handle stain variation for segmentation tasks, comparing ten methods on Masson's trichrome and H&E stained cell and nuclei datasets, respectively. We observed that stain normalisation methods resulted in equivalent or worse performance, while stain augmentation or stain adversarial methods demonstrated improved performance, with the best performance consistently achieved by our proposed approach. The code is available at: https://github.com/mlyg/stain_consistency_learning