For some reason the usual options when highlighting the Gas Mask with a gamepad (such as Inspect, Equip, Drop, etc) have been replaced with one saying "Pick Up" (See screenshot). Pressing the button seems to then make the character walk in a random direction. The mask can still equipped by moving it over to the head slot but there is no way of dropping it other than storing it an external inventory.
I believe it started happening after taking the Gas Mask off the shelf in my house (although I didn't notice at first). I used a gamepad to replace an item on the shelf with the Gas Mask. Taking the Gas Mask from the shelf again seemed to cause the problem.