I would replace the bearing(s). Too much play in the bearings allowing the axles to wobble is one of the reasons why the rear axle seal fails. Your Tundra doesn't have a million miles and hasn't been abused, so stuff like flexing of the housing doesn't make a lot of sense. OTOH my axle was still running the bearings that Toyota put in up until a couple of years ago, so anything's possible.
'91 Toyota Pickup
'09 Kawasaki KLR650
'12 Gunnar Rockhound 29
“Anyone who believes in indefinite growth in anything physical, on a physically finite planet, is either mad or an economist.” -- Kenneth E. Boulding