Existing rotation-invariant point cloud masked autoencoders (MAE) rely on random masking strategies that overlook geometric structure and semantic coherence. Random masking treats patches independently, failing to capture spatial relationships consistent across orientations and overlooking semantic object parts that maintain identity regardless of rotation. We propose a dual-stream masking approach combining 3D Spatial Grid Masking and Progressive Semantic Masking to address these fundamental limitations. Grid masking creates structured patterns through coordinate sorting to capture geometric relationships that persist across different orientations, while semantic masking uses attention-driven clustering to discover semantically meaningful parts and maintain their coherence during masking. These complementary streams are orchestrated via curriculum learning with dynamic weighting, progressing from geometric understanding to semantic discovery. Designed as plug-and-play components, our strategies integrate into existing rotation-invariant frameworks without architectural changes, ensuring broad compatibility across different approaches. Comprehensive experiments on ModelNet40, ScanObjectNN, and OmniObject3D demonstrate consistent improvements across various rotation scenarios, showing substantial performance gains over the baseline rotation-invariant methods.