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Industrial insertion tasks are often performed repetitively with parts that are subject to tight tolerances and prone to breakage. Learning an industrial insertion policy in real is challenging as the collision between the parts and the environment can cause slippage or breakage of the part. In this paper, we present a safe self-supervised method to learn a visuo-tactile insertion policy that is robust to grasp pose variations. The method reduces human input and collisions between the part and the receptacle. The method divides the insertion task into two phases. In the first align phase, a tactile-based grasp pose estimation model is learned to align the insertion part with the receptacle. In the second insert phase, a vision-based policy is learned to guide the part into the receptacle. The robot uses force-torque sensing to achieve a safe self-supervised data collection pipeline. Physical experiments on the USB insertion task from the NIST Assembly Taskboard suggest that the resulting policies can achieve 45/45 insertion successes on 45 different initial grasp poses, improving on two baselines: (1) a behavior cloning agent trained on 50 human insertion demonstrations (1/45) and (2) an online RL policy (TD3) trained in real (0/45).