Remote sensing imagery poses a distinct challenge for semantic segmentation due to its inherent fractal complexity and the diversity of geometric structures present in real-world geospatial scenes. Conventional Euclidean-based models typically assume spatial uniformity; however, such assumptions often break down when confronted with objects exhibiting markedly different structural characteristics—such as roads versus vegetation—thereby complicating the feature representation process. Hyperbolic space offers a theoretically grounded alternative for modeling such hierarchical and heterogeneous patterns, yet fully replacing Euclidean geometry incurs significant computational overhead. To address this trade-off, we propose Geometry-Aware Adaptive Routing (GAAR), a novel module that facilitates Hyperbolic-aware routing by dynamically allocating high-level features to either Euclidean or Hyperbolic subspaces through a learnable binary gating mechanism, informed by structural priors learned during training. To further promote routing stability and geometric consistency, we introduce Geometry-Aware Deterministic Regularization (GADR), a regularization strategy that encourages confident, structure-aligned assignments. GAAR is plug-and-play and integrates seamlessly into existing segmentation architectures. Experiments on three challenging Remote Sensing Image Semantic Segmentation (RSISS) benchmarks demonstrate that our approach consistently outperforms state-of-the-art (SOTA) methods, particularly in geometrically complex regions, offering a scalable and effective solution to the limitations of purely Euclidean modeling. Code and models will be released upon acceptance.