Endowing robots with tactile capabilities opens up new possibilities for their interaction with the environment, including the ability to handle fragile and/or soft objects. In this work, we equip the robot gripper with low-cost vision-based tactile sensors and propose a manipulation algorithm that adapts to both rigid and soft objects without requiring any knowledge of their properties. The algorithm relies on a touch and slip detection method, which considers the variation in the tactile images with respect to reference ones. We validate the approach on seven different objects, with different properties in terms of rigidity and fragility, to perform unplugging and lifting tasks. Furthermore, to enhance applicability, we combine the manipulation algorithm with a grasp sampler for the task of finding and picking a grape from a bunch without damaging it.