The precise segmentation of geological linear features, spanning from planetary lineaments to terrestrial fractures, demands capturing long-range dependencies across complex anisotropic topologies. Although State Space Models (SSMs) offer near-linear computational complexity, their dependence on rigid, axis-aligned scanning trajectories induces a fundamental topological mismatch with curvilinear targets, resulting in fragmented context and feature erosion. To bridge this gap, we propose Fluxamba, a lightweight architecture that introduces a topology-aware feature rectification framework. Central to our design is the Structural Flux Block (SFB), which orchestrates an anisotropic information flux by integrating an Anisotropic Structural Gate (ASG) with a Prior-Modulated Flow (PMF). This mechanism decouples feature orientation from spatial location, dynamically gating context aggregation along the target's intrinsic geometry rather than rigid paths. Furthermore, to mitigate serialization-induced noise in low-contrast environments, we incorporate a Hierarchical Spatial Regulator (HSR) for multi-scale semantic alignment and a High-Fidelity Focus Unit (HFFU) to explicitly maximize the signal-to-noise ratio of faint features. Extensive experiments on diverse geological benchmarks (LROC-Lineament, LineaMapper, and GeoCrack) demonstrate that Fluxamba establishes a new state-of-the-art. Notably, on the challenging LROC-Lineament dataset, it achieves an F1-score of 89.22% and mIoU of 89.87%. Achieving a real-time inference speed of over 24 FPS with only 3.4M parameters and 6.3G FLOPs, Fluxamba reduces computational costs by up to two orders of magnitude compared to heavy-weight baselines, thereby establishing a new Pareto frontier between segmentation fidelity and onboard deployment feasibility.