Robotic manipulators navigating cluttered shelves or cabinets may find it challenging to avoid contact with obstacles. Indeed, rearranging obstacles may be necessary to access a target. Rather than planning explicit motions that place obstacles into a desired pose, we suggest allowing incidental contacts to rearrange obstacles while monitoring contacts for safety. Bypassing object identification, we present a method for categorizing object motions from tactile data collected from incidental contacts with a capacitive tactile skin on an Allegro Hand. We formalize tactile cues associated with categories of object motion, demonstrating that they can determine with $>90$% accuracy whether an object is movable and whether a contact is causing the object to slide stably (safe contact) or tip (unsafe).