I am a father of two kids. I can be walking on the sidewalk with my kids, and see another parent, maybe a mom, smile and say hello, it's totally fine.
Same situation, but maybe my kids are not with me, maybe they're in school. Suddenly I'm a strange man saying hello at a mom and her kids. A real danger situation! Hold onto your bag, hold the kids extra tight, reach for the pepper spray. But I am the same person in both situations.
But mindful of this, I keep a respectful distance in the latter case.
From time to time, a colleague brings their child to work (because childcare fell through, or something), and they get to interact with strangers! It's weird, they are afraid, they don't know what to say, they generally don't know how to conduct themselves. Oftentimes they are distractingly loud, can't entertain themselves and generally annoy everyone within earshot. And since you are not a parent you are not supposed to discipline the little shits!
Soon they are teenagers and enter the working environment, still without social experience. The Apocalypse is on its way.
and to the OP's point, i'm not a particularly social person, but i love smiling and waving at babies. it's as rewarding to you as it is to the baby. =)
On the other hand if you remove the question of gender I would have to admit that many in the US are more guarded with strangers than people tend to be in other places I've been.
I say good morning to most people I see, we are friendly here in South Wales, but I don’t risk appearing on anyone’s microaggression blog or outrage twitter.
It was a way of selling newspapers.
So now you have to have kids of your own in proximity or grandchildren in proximity to be part of the club of people allowed to speak with a child. Failing that you need a full criminal records check.
During my own childhood I was out and about all hours of day and night delivering newspapers, babysitting, doing gardening jobs, walking/cycling/hitching to get to places generally alone. We didn't have the 'p' word back then and a certain amount of being sensible was expected. Not so long ago I had a chat with my sister about who had an un-natural interest in our childhood selves in the village and neighbouring area. The list was quite a long one, my sister being exposed to by people I considered normal and vice-versa.
We even had Fred West - a notorious murderer - parked up in his van at a local spot. Being lured in to a house or a strange car was just one of those things to watch out for, plus people would give you strange gifts.
But the thing was that we - my sister and myself - were the local community. If anything did happen to us then you could guarantee that someone would call our mum to complain they had not had their paper delivered, or someone would see us enter a house to not exit. For us it would be impossible for us to travel anywhere without being observed. Hitch-hiking was also something we did, but when you know half the cars on the road then you expect a lift.
We actually interacted with the crazies fully knowing that there wasn't something quite right about them. We also told our mum about unwanted advances and strange gifts that came our way. Our mother never got the police involved. In our recent recollections there were a dozen or so where a line had been crossed or other evidence existed. Would the community have been better had there been court cases? Not really, common sense by us and the fact that it was a community worked.
Had the moral panic existed then and had we been locked away lest we meet someone that smiled at kids then we would have also lost out from the kind grown-ups that went the extra mile for us. We could get lifts into town, every school history project was done with the help of some local senior citizen, to earn money we had to do no more than walk out the door and, for every weird person there were a dozen that would be looking out for us.