I wouldn’t let a 4-year-old run through an entire museum, period. Nor would I expect them to keep their hands behind their backs while walking. But I ask my kids to keep their hands behind their backs while looking at objects in museums and galleries that are within arm’s reach. I often do it myself, too. That’s in addition to (not instead of) supervising them. When looking at something, it’s natural for kids (and adults) to want to touch and point (pointing can easily turn into inadvertent touching), and I don’t have the Jedi reflexes to stop a little hand from jabbing out and scraping paint off of a painting or knocking something over.
“Museum hands” isn’t being mean to kids. It’s a practical way to allow young kids to see amazing things without breaking anything.
