It is widely known that males and females typically possess different sound characteristics when singing, such as timbre and pitch, but it has never been explored whether these gender-based characteristics lead to a performance disparity in singing voice transcription (SVT), whose target includes pitch. Such a disparity could cause fairness issues and severely affect the user experience of downstream SVT applications. Motivated by this, we first demonstrate the female superiority of SVT systems, which is observed across different models and datasets. We find that different pitch distributions, rather than gender data imbalance, contribute to this disparity. To address this issue, we propose using an attribute predictor to predict gender labels and adversarially training the SVT system to enforce the gender-invariance of acoustic representations. Leveraging the prior knowledge that pitch distributions may contribute to the gender bias, we propose conditionally aligning acoustic representations between demographic groups by feeding note events to the attribute predictor. Empirical experiments on multiple benchmark SVT datasets show that our method significantly reduces gender bias (up to more than 50%) with negligible degradation of overall SVT performance, on both in-domain and out-of-domain singing data, thus offering a better fairness-utility trade-off.