Deep learning (DL) has been increasingly applied in medical imaging, however, it requires large amounts of data, which raises many challenges related to data privacy, storage, and transfer. Federated learning (FL) is a training paradigm that overcomes these issues, though its effectiveness may be reduced when dealing with non-independent and identically distributed (non-IID) data. This study simulates non-IID conditions by applying different MRI intensity normalization techniques to separate data subsets, reflecting a common cause of heterogeneity. These subsets are then used for training and testing models for brain tumor segmentation. The findings provide insights into the influence of the MRI intensity normalization methods on segmentation models, both training and inference. Notably, the FL methods demonstrated resilience to inconsistently normalized data across clients, achieving the 3D Dice score of 92%, which is comparable to a centralized model (trained using all data). These results indicate that FL is a solution to effectively train high-performing models without violating data privacy, a crucial concern in medical applications. The code is available at: https://github.com/SanoScience/fl-varying-normalization.