This paper addresses semantic planning problems in unknown environments under perceptual uncertainty. The environment contains multiple unknown semantically labeled regions or objects, and the robot must reach desired locations while maintaining class-dependent distances from them. We aim to compute robot paths that complete such semantic reach-avoid tasks with user-defined probability despite uncertain perception. Existing planning algorithms either ignore perceptual uncertainty, thus lacking correctness guarantees, or assume known sensor models and noise characteristics. In contrast, we present the first planner for semantic reach-avoid tasks that achieves user-specified mission completion rates without requiring any knowledge of sensor models or noise. This is enabled by quantifying uncertainty in semantic maps, constructed on-the-fly from perceptual measurements, using conformal prediction in a model and distribution free manner. We validate our approach and the theoretical mission completion rates through extensive experiments, showing that it consistently outperforms baselines in mission success rates.