I agree that the appearance of crabbing may be an optical illusion due to the difference in track width.
But the OP seems to be saying the rear axle is shifting side to side when driving. I don't see how something like that could get past a suspension shop rebuild and later inspection, but it certainly isn't right. But then it's hard to tell if he's saying the axle moves relative to the truck (my interpretation) or the rear of the truck moves relative to the front (the illusion).
jefffoxsr wrote:
There is lateral movement in the rear of the truck when the road changes so something is wrong. It should not be doing this
If the rear was moving relative to the front on a scale large enough to notice from a following vehicle I'd think the driver would notice an awfully squirrelly ride.