In this paper, we consider a Micro Aerial Vehicle (MAV) system teleoperated by a non-expert and introduce a perceptive safety filter that leverages Control Barrier Functions (CBFs) in conjunction with Visual-Inertial Simultaneous Localization and Mapping (VI-SLAM) and dense 3D occupancy mapping to guarantee safe navigation in complex and unstructured environments. Our system relies solely on onboard IMU measurements, stereo infrared images, and depth images and autonomously corrects teleoperated inputs when they are deemed unsafe. We define a point in 3D space as unsafe if it satisfies either of two conditions: (i) it is occupied by an obstacle, or (ii) it remains unmapped. At each time step, an occupancy map of the environment is updated by the VI-SLAM by fusing the onboard measurements, and a CBF is constructed to parameterize the (un)safe region in the 3D space. Given the CBF and state feedback from the VI-SLAM module, a safety filter computes a certified reference that best matches the teleoperation input while satisfying the safety constraint encoded by the CBF. In contrast to existing perception-based safe control frameworks, we directly close the perception-action loop and demonstrate the full capability of safe control in combination with real-time VI-SLAM without any external infrastructure or prior knowledge of the environment. We verify the efficacy of the perceptive safety filter in real-time MAV experiments using exclusively onboard sensing and computation and show that the teleoperated MAV is able to safely navigate through unknown environments despite arbitrary inputs sent by the teleoperator.