Respiratory monitoring is an extremely important task in modern medical services. Due to its significant advantages, e.g., non-contact, radar-based respiratory monitoring has attracted widespread attention from both academia and industry. Unfortunately, though it can achieve high monitoring accuracy, consumer electronics-grade radar data inevitably contains User-sensitive Identity Information (USI), which may be maliciously used and further lead to privacy leakage. To track these challenges, by variational mode decomposition (VMD) and adversarial loss-based encryption, we propose a novel Trusted Respiratory Monitoring paradigm, Tru-RM, to perform automated respiratory monitoring through radio signals while effectively anonymizing USI. The key enablers of Tru-RM are Attribute Feature Decoupling (AFD), Flexible Perturbation Encryptor (FPE), and robust Perturbation Tolerable Network (PTN) used for attribute decomposition, identity encryption, and perturbed respiratory monitoring, respectively. Specifically, AFD is designed to decompose the raw radar signals into the universal respiratory component, the personal difference component, and other unrelated components. Then, by using large noise to drown out the other unrelated components, and the phase noise algorithm with a learning intensity parameter to eliminate USI in the personal difference component, FPE is designed to achieve complete user identity information encryption without affecting respiratory features. Finally, by designing the transferred generalized domain-independent network, PTN is employed to accurately detect respiration when waveforms change significantly. Extensive experiments based on various detection distances, respiratory patterns, and durations demonstrate the superior performance of Tru-RM on strong anonymity of USI, and high detection accuracy of perturbed respiratory waveforms.