I used to run three non-profit playgroups a week. Some kids make it like the movie Lord of The Flies! But you can always see where they get it. Mums/dads/GPs can be a bloody nightmare. One little boy was often violent towards all the other children (in a quite frankly, disturbing way!) and when you met the mum you could tell why. She wasn't violent though, never told him off, spanked him, shouted or anything. She was permissive. She'd smile sweetly, proudly watching him shove a just started walking baby at the ground. Repeatedly. It. Was. Nuts.
She honestly didn't think her little Dudley Dursley could do any wrong. If he punched a kid in the stomach it was because that boy obviously hit him first (they never did). If he gouged at a toddler's eye it was a "boys will be boys" thing. If he snatched a toy then it was because they weren't sharing and were being mean.
One time I watched her go up to a small child, lift them off one of the two red cars and place him, now wailing, on the floor and hand the car to her son. The other car was available but her boy didn't want that one.
He's almost a high schooler now. Throughout the whole 7 years of primary(s) he was most kid's nightmare. And he got away with it because his mum was a local teacher. Ironically she was quite the cow of a teacher too. Very shouty and strict. As long as it was never her kids of course.
OP, don't worry about what everyone else is doing. Just make sure your kids are strictly observed and corrected quickly because the last thing you want is a petty mum using any of your child's innocent transgressions to be used as an excuse to treat them poorly. And if they're acting childishly towards your child for no reason (it does happen) then simply tell your child what's going on, loud enough for people to hear.
"I know darling, some people do things like that. It's very silly so let's just leave them to it and go do xxx or xxx"