I think taking away the mystery and the OHH factor is very important. I have taught my boys that guns are just dangerous tools. If they want to go shooting we go shooting. If one of their friends was showing off a gun I think they would be the first to say put it away.
Every range session starts with a safety briefing, only one person fires at a time. I am usually right behind my younger boys. My teenager is capable of shooting without direct supervision.
We practice range safety, I have had my kids correct friends of mine while out target practicing.
Whenever someone shoots a new gun there is only 1 round loaded. I don't press my kids to shoot anything they don't want to.
I would say talk to your neighbor in a friendly way, shooting with kids is great common ground for a conversation. It shouldn't be too hard to pick his brain, and see if your views line up. Just because he posted one possibly irresponsible picture is no need to panic.