Beamforming designs for integrated sensing and communication (ISAC) in cell-free multiple-input multiple-output (MIMO) systems face the challenge to stay reliable under uncertainties from both channel state information (CSI) as well as clutter. To this end, this paper proposes an impairment-aware heterogeneous graph neural network (GNN) framework for beamforming that obtains the CSI error level and the clutter covariance as edge features, which enables a single trained model to adapt to both impairments. In particular, the GNN is trained on a low quantile of the minimum user rate with a clutter-aware signal-to-clutter-plus-noise ratio, balanced by a normalized Tchebycheff scalarization. Simulation results show that the proposed GNN framework outperforms the considered baselines in sensing-only and communication-only settings. Depending on the operating point, a single GNN model attains approximately 97\% of each baseline's rate while serving both functionalities at once. The model further generalizes to unseen CSI error levels and clutter counts and renders the ISAC system resilient.

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