We introduce the first active learning (AL) model for high-accuracy instance segmentation of moveable parts from RGB images of real indoor scenes. Specifically, our goal is to obtain fully validated segmentation results by humans while minimizing manual effort. To this end, we employ a transformer that utilizes a masked-attention mechanism to supervise the active segmentation. To enhance the network tailored to moveable parts, we introduce a coarse-to-fine AL approach which first uses an object-aware masked attention and then a pose-aware one, leveraging the hierarchical nature of the problem and a correlation between moveable parts and object poses and interaction directions. When applying our AL model to 2,000 real images, we obtain fully validated moveable part segmentations with semantic labels, by only needing to manually annotate 11.45% of the images. This translates to significant (60%) time saving over manual effort required by the best non-AL model to attain the same segmentation accuracy. At last, we contribute a dataset of 2,550 real images with annotated moveable parts, demonstrating its superior quality and diversity over the best alternatives.