Rubber tree is one of the essential tropical economic crops, and rubber tree powdery mildew (PM) is the most damaging disease to the growth of rubber trees. Accurate and timely detection of PM is the key to preventing the large-scale spread of PM. Recently, unmanned aerial vehicle (UAV) remote sensing technology has been widely used in the field of agroforestry. The objective of this study was to establish a method for identifying rubber trees infected or uninfected by PM using UAV-based multispectral images. We resampled the original multispectral image with 3.4 cm spatial resolution to multispectral images with different spatial resolutions (7 cm, 14 cm, and 30 cm) using the nearest neighbor method, extracted 22 vegetation index features and 40 texture features to construct the initial feature space, and then used the SPA, ReliefF, and Boruta–SHAP algorithms to optimize the feature space. Finally, a rubber tree PM monitoring model was constructed based on the optimized features as input combined with KNN, RF, and SVM algorithms. The results show that the simulation of images with different spatial resolutions indicates that, with resolutions higher than 7 cm, a promising classification result (>90%) is achieved in all feature sets and three optimized feature subsets, in which the 3.4 cm resolution is the highest and better than 7 cm, 14 cm, and 30 cm. Meanwhile, the best classification accuracy was achieved by combining the Boruta–SHAP optimized feature subset and SVM model, which were 98.16%, 96.32%, 95.71%, and 88.34% at 3.4 cm, 7 cm, 14 cm, and 30 cm resolutions, respectively. Compared with SPA–SVM and ReliefF–SVM, the classification accuracy was improved by 6.14%, 5.52%, 12.89%, and 9.2% and 1.84%, 0.61%, 1.23%, and 6.13%, respectively. This study’s results will guide rubber tree plantation management and PM monitoring.