Many US museums permit backpacks only when they are carried on one shoulder. Here are some examples:
Backpacks and large bags must be checked. Smaller bags may be carried on one shoulder or handheld.
Bags larger than a standard backpack need to be checked into coat check. Any backpack sizes or smaller can be worn on one shoulder.
Backpacks may not be worn on the back, but must be carried on the side, under the arm, or on the front of the body.
There's a number of additional sources quoting this requirement:
security people DID let me take it in as long as I kept it slung over ONLY ONE SHOULDER
I get the impression that things meant to be carried on one shoulder or in the hand are typically OK, while things that go over two shoulders are not.
Why is that? I first thought it's an easy way of implementing a size/weight limit. However, personal experience shows me that even when you are allowed to bring a backpack that is small enough to be carried on one shoulder, you have to wear it on one shoulder the all the time.
One possible reason is given here, but it's not very convincing to me:
Packs on the back are risks for the art. People turn around quickly and knock statues or scratch paintings with the packs when worn on two shoulders across the back.