Feature-based anomaly detection is widely adopted in industrial inspection due to the strong representational power of large pre-trained vision encoders. While most existing methods focus on improving within-category anomaly scoring, practical deployments increasingly require task-agnostic operation under continual category expansion, where the category identity is unknown at test time. In this setting, overall performance is often dominated by expert selection, namely routing an input to an appropriate normality model before any head-specific scoring is applied. However, routing rules that compare head-specific anomaly scores across independently constructed heads are unreliable in practice, as score distributions can differ substantially across categories in scale and tail behavior. We propose GCR, a lightweight mixture-of-experts framework for stabilizing task-agnostic continual anomaly detection through geometry-consistent routing. GCR routes each test image directly in a shared frozen patch-embedding space by minimizing an accumulated nearest-prototype distance to category-specific prototype banks, and then computes anomaly maps only within the routed expert using a standard prototype-based scoring rule. By separating cross-head decision making from within-head anomaly scoring, GCR avoids cross-head score comparability issues without requiring end-to-end representation learning. Experiments on MVTec AD and VisA show that geometry-consistent routing substantially improves routing stability and mitigates continual performance collapse, achieving near-zero forgetting while maintaining competitive detection and localization performance. These results indicate that many failures previously attributed to representation forgetting can instead be explained by decision-rule instability in cross-head routing. Code is available at https://github.com/jw-chae/GCR