Recently, the ever-growing demand for privacy-oriented machine learning has motivated researchers to develop federated and decentralized learning techniques, allowing individual clients to train models collaboratively without disclosing their private datasets. However, widespread adoption has been limited in domains relying on high levels of user trust, where assessment of data compatibility is essential. In this work, we define and address low interoperability induced by underlying client data inconsistencies in federated learning for tabular data. The proposed method, iFedAvg, builds on federated averaging adding local element-wise affine layers to allow for a personalized and granular understanding of the collaborative learning process. Thus, enabling the detection of outlier datasets in the federation and also learning the compensation for local data distribution shifts without sharing any original data. We evaluate iFedAvg using several public benchmarks and a previously unstudied collection of real-world datasets from the 2014 - 2016 West African Ebola epidemic, jointly forming the largest such dataset in the world. In all evaluations, iFedAvg achieves competitive average performance with negligible overhead. It additionally shows substantial improvement on outlier clients, highlighting increased robustness to individual dataset shifts. Most importantly, our method provides valuable client-specific insights at a fine-grained level to guide interoperable federated learning.