Music aesthetics scoring plays a critical role in applications such as dataset curation, generative model evaluation, and reward modeling for music generation. Recent approaches rely on deep neural networks trained on human-annotated ratings, but these models may exploit spurious correlations rather than capturing perceptually meaningful aesthetics. In this work, we identify a previously underexplored failure mode in music evaluation models: genre-induced shortcut learning. Through a systematic analysis of SongEval, we show that biases in training data lead to strong correlations between genre-related features and predicted scores, causing the model to use them as a proxy for aesthetics. This results in systematic overestimation of pop music and undervaluation of high-quality samples from other genres, leading to predictions that are inconsistent with human preferences. To address this issue, we propose a training objective that jointly reweights hard samples and regularizes group-level performance, encouraging the model to learn genre-invariant representations of musicality. Experimental results demonstrate that our method reduces genre-dependent bias and improves alignment with human preferences, as reflected by gains in both cross-genre and within-genre preference alignment.