Graph filters that transform prior node values to posterior scores via edge propagation often support graph mining tasks affecting humans, such as recommendation and ranking. Thus, it is important to make them fair in terms of satisfying statistical parity constraints between groups of nodes (e.g., distribute score mass between genders proportionally to their representation). To achieve this while minimally perturbing the original posteriors, we introduce a filter-aware universal approximation framework for posterior objectives. This defines appropriate graph neural networks trained at runtime to be similar to filters but also locally optimize a large class of objectives, including fairness-aware ones. Experiments on a collection of 8 filters and 5 graphs show that our approach performs equally well or better than alternatives in meeting parity constraints while preserving the AUC of score-based community member recommendation and creating minimal utility loss in prior diffusion.