Deep neural networks have been applied to audio spectrograms for respiratory sound classification, but it is still remains challenging to achieve satisfactory performance due to the scarcity of available data. Moreover, domain mismatch may be introduced into the trained models as a result of the respiratory sound samples being collected from various electronic stethoscopes, patient demographics, and recording environments. To tackle this issue, we proposed a modified Masked Autoencoder (MAE) model, named Disentangling Dual-Encoder MAE (DDE-MAE) for respiratory sound classification. Two independent encoders were designed to capture disease-related and disease-irrelevant information separately, achieving feature disentanglement to reduce the domain mismatch. Our method achieves a competitive performance on the ICBHI dataset.