Federated learning is a decentralized collaborative training paradigm preserving stakeholders' data ownership while improving performance and generalization. However, statistical heterogeneity among client datasets degrades system performance. To address this issue, we propose Adaptive Normalization-free Feature Recalibration (ANFR), a model architecture-level approach that combines weight standardization and channel attention to combat heterogeneous data in FL. ANFR leverages weight standardization to avoid mismatched client statistics and inconsistent averaging, ensuring robustness under heterogeneity, and channel attention to produce learnable scaling factors for feature maps, suppressing inconsistencies across clients due to heterogeneity. We demonstrate that combining these techniques boosts model performance beyond their individual contributions, by improving class selectivity and channel attention weight distribution. ANFR works with any aggregation method, supports both global and personalized FL, and adds minimal overhead. Furthermore, when training with differential privacy, ANFR achieves an appealing balance between privacy and utility, enabling strong privacy guarantees without sacrificing performance. By integrating weight standardization and channel attention in the backbone model, ANFR offers a novel and versatile approach to the challenge of statistical heterogeneity. Extensive experiments show ANFR consistently outperforms established baselines across various aggregation methods, datasets, and heterogeneity conditions. Code is provided at https://github.com/siomvas/ANFR.