High-level Autonomous Driving Systems (ADSs), such as Google Waymo and Baidu Apollo, typically rely on multi-sensor fusion (MSF) based approaches to perceive their surroundings. This strategy increases perception robustness by combining the respective strengths of the camera and LiDAR and directly affects the safety-critical driving decisions of autonomous vehicles (AVs). However, in real-world autonomous driving scenarios, cameras and LiDAR are subject to various faults, which can probably significantly impact the decision-making and behaviors of ADSs. Existing MSF testing approaches only discovered corner cases that the MSF-based perception cannot accurately detected by MSF-based perception, while lacking research on how sensor faults affect the system-level behaviors of ADSs. To address this gap, we conduct the first exploration of the fault tolerance of MSF perception-based ADS for sensor faults. In this paper, we systematically and comprehensively build fault models for cameras and LiDAR in AVs and inject them into the MSF perception-based ADS to test its behaviors in test scenarios. To effectively and efficiently explore the parameter spaces of sensor fault models, we design a feedback-guided differential fuzzer to discover the safety violations of MSF perception-based ADS caused by the injected sensor faults. We evaluate FADE on the representative and practical industrial ADS, Baidu Apollo. Our evaluation results demonstrate the effectiveness and efficiency of FADE, and we conclude some useful findings from the experimental results. To validate the findings in the physical world, we use a real Baidu Apollo 6.0 EDU autonomous vehicle to conduct the physical experiments, and the results show the practical significance of our findings.