Federated- and Continual Learning have been established as approaches to enable privacy-aware learning on continuously changing data, as required for deploying AI systems in histopathology images. However, data shifts can occur in a dynamic world, spatially between institutions and temporally, due to changing data over time. This leads to two issues: Client Drift, where the central model degrades from aggregating data from clients trained on shifted data, and Catastrophic Forgetting, from temporal shifts such as changes in patient populations. Both tend to degrade the model's performance of previously seen data or spatially distributed training. Despite both problems arising from the same underlying problem of data shifts, existing research addresses them only individually. In this work, we introduce a method that can jointly alleviate Client Drift and Catastrophic Forgetting by using our proposed Dynamic Barlow Continuity that evaluates client updates on a public reference dataset and uses this to guide the training process to a spatially and temporally shift-invariant model. We evaluate our approach on the histopathology datasets BCSS and Semicol and prove our method to be highly effective by jointly improving the dice score as much as from 15.8% to 71.6% in Client Drift and from 42.5% to 62.8% in Catastrophic Forgetting. This enables Dynamic Learning by establishing spatio-temporal shift-invariance.