Just FWIW: in 1970 or so I got a Nylon 66 for Christmas, at the age of 12 or 13. On the day after Xmas, a friend's father was going to drive out to the Rod-n-Gun. They lived a couple of miles across town.
I didn't own a case or sling. I put a box of shells in my pocket, got the rifle, and headed across town through residential neighborhoods. On the way, there was an elementary school with a large campus - maybe 1/2 mile by 1/3 mile. The shortest route happened to be diagonally across the schoolyard.
As luck would have it, as I crossed the street by the corner of the schoolyard, a police car pulled up. I was carrying the rifle more or less horizontally with one hand around the receiver. As I crossed in front of the police car, I gave him a big smile and wave, and he returned both. It was a regular Norman Rockwell moment - a kid gets his 1st 22 rifle for Xmas.
Reading this thread, I see a lot of people saying that having an unslung or uncased rifle is obviously suspicious. I disagree.
I don't know the kid's demeanor or behavior. Maybe he was doing something that would make a reasonable officer ask questions, or maybe he wasn't. But on that winter's day, that officer earned his pay by correctly inferring 'Kid with a Christmas present'. It doesn't make a better world if he reflexively called for backup and did a felony stop and hauled me off to jail.
Thank you for this powerful anecdote.