Deep learning-based models in medical imaging often struggle to generalize effectively to new scans due to data heterogeneity arising from differences in hardware, acquisition parameters, population, and artifacts. This limitation presents a significant challenge in adopting machine learning models for clinical practice. We propose an unsupervised method for robust domain adaptation in brain MRI segmentation by leveraging MRI-specific augmentation techniques. To evaluate the effectiveness of our method, we conduct extensive experiments across diverse datasets, modalities, and segmentation tasks, comparing against the state-of-the-art methods. The results show that our proposed approach achieves high accuracy, exhibits broad applicability, and showcases remarkable robustness against domain shift in various tasks, surpassing the state-of-the-art performance in the majority of cases.