It seems that bags I pull out of my moving boxes (boxes I've picked up but not yet emptied) have a strange property that makes them invisible when they're in my inventory. They can't be interacted with (no clicking on them or dragging things into them), but they can be opened by searching for their name and then choosing "Open", at which point I can work with the contents.
Here's a pic of an open one (bag is in the first inventory slot).
Things placed in the bag are also invisible (there are items in the two far-right slots, though you can't tell from the picture).