Exercise-induced sudden death has become an increasingly serious health issue in recent years. Fortunately, respiratory monitoring can serve as an effective early prevention solution. In particular, radio frequency (RF) sensing has emerged as a promising solution due to its contactless nature and privacy preservation. Existing RF-based respiratory monitoring solutions for homes, offices, or vehicles would suffer from significant performance degradation when deployed in typical gym workouts, where respiratory and physical movements are mixed in the RF signals in an unpredictable manner, leading to a blind source separation (BSS) problem. What is worse, the prior assumptions of source independence in existing BSS algorithms no longer hold, leaving respiratory monitoring in gym scenarios as an open issue. In this paper, we propose RF-GymCare, which introduces respiratory priors into the BSS problem and utilizes knowledge distillation to transfer these priors, aiming to learn the demixing weight from mixed signals. With the demixing weight, the respiratory signal can be obtained through a linear combination of the mixed signals. Our experiments with 13 hours of data across nine types of exercises demonstrate its superiority over existing methods, achieving a median similarity of 0.75 and a median rate error of 0.5 respiration per minute (RPM), respectively.