Short answer? The white wires are simply duplicate ground connections.
Long answer in case you care? Look at your last picture. You can see the following stuff. The fixture has two bulb sockets. One of them holds a dual-filament bulb (two bulbs in one glass globe), so the fixture needs three hot feeds. These are the red, green, and black wires. Each of the bulbs also needs to have its metal shell grounded, so both bulbs are attached to the metal plates that are partially visible beneath the glass globes of the bulbs. Now look at your second picture. Many RVs put screws through the plastic towers just below the riveted white-wire connections, and into the metal skin of the trailer. The screws contact the metal plates on their way through, as well as the metal skin of the trailer, completing the ground connection. In other RVs, it might be that the extra screws are not used, or the trailer skin is fiberglass, or the metal skin is not grounded. So the maker of the fixture provides the white wires as an additional alternate way to make the ground connection. I believe that TM mounts the fixtures at the four corners, but I don't recall if they put additional screws through the holes near the rivets. If yes, then the ground connection is made by those screws, and you can simply insulate and tie off the white wires. If not, you could either run new screws through the holes near the rivets, or you could put the end of one of the white wires around one of the corner screws - screws which go through the aluminum skin of the TM.
