Identifiable causal representation learning seeks to uncover the true causal relationships underlying a data generation process. In medical imaging, this presents opportunities to improve the generalisability and robustness of task-specific latent features. This work introduces the concept of grouping observations to learn identifiable representations for disease classification in chest X-rays via an end-to-end framework. Our experiments demonstrate that these causal representations improve generalisability and robustness across multiple classification tasks when grouping is used to enforce invariance w.r.t race, sex, and imaging views.