Multistage compressors are widely used in essential equipment such as aero-engines, gas turbines, and industrial compressors. However, there are hundreds of geometric deviations with uncertain characteristics in the manufacture and maintenance of multistage compressors, resulting in severe performance dispersion. If the geometric deviation is strictly controlled, the performance dispersion can be effectively controlled, but the manufacturing and maintenance costs are high; otherwise, the costs can be reduced, but the performance dispersion is large. To solve the above contradictions and realize the synergistic optimization of the performance and cost of multistage compressor manufacture and maintenance, it is necessary to accurately identify critical geometric features affecting the performance dispersion from the numerous features. Then only the critical features are strictly controlled rather than all features. In this paper, combining the neural network and interpretable machine learning methods, a feature selection method based on the bidirectional search is developed to achieve fast and accurate identification of critical geometric features in multistage compressors. This method is applied to a 3-stage compressor. Fifteen critical features are accurately identified from the original 291 geometric uncertainty features to control the mass flow rate dispersion. When reducing the deviation ranges of the 15 features to half, the mass flow rate dispersion can be reduced by 48%, while reducing the deviation ranges of the other 276 features to half, the dispersion can only be reduced by 5%. For efficiency dispersion control, 60 critical geometric features are accurately identified from the original 291 geometric uncertainty features. When reducing the deviation ranges of the 60 features to half, the efficiency dispersion can be reduced by 35%, while reducing the deviation ranges of the other 231 features to half, the dispersion can only be reduced by 14%. This paper proposed a performance dispersion control method for multistage compressors based on the accurate identification of critical features. This method can provide an effective solution for the performance dispersion control in multistage compressor manufacture and maintenance, which lays the foundation for the collaborative optimization of compressor performance and cost.