If it's not Hurting People or Property
When I feel like I need to jump in and stop children in their tracks, I stop first and ask myself, "Are they hurting people or property? Are they exhibiting bad manners for this location?" If not then I leave them alone. Play is important work, and adults often interfere in this work for the wrong reasons.
A toddler is jumping in a mud puddle
Stop! You are going to be muddy and cold!
Is the child going to get hurt? No. They'll get dirty but dirt can be washed. They may get a bit chilly but not dangerously so, and it's a good natural lesson for them. No other people are in the splash zone.
Is the property going to be hurt? Nope it's just water on the sidewalk. The child is wearing play clothes, nothing fancy that can't be washed.
Is this bad manners? No. It's a rainy day, we are out for a walk. No plans to go somewhere fancy. I have a change of clothes with me.
Child refuses to put a coat on
You will be cold. You have to wear a coat
Will people be hurt: the child will get cold. It's really cold outside
Will property be hurt: No
Is it bad manners for the situation: No
Tell the child safety comes first. They have to bring the coat with them, but they can decide when they are ready to wear it.
Child decides to climb a tree at the park
That's not safe! You could fall!
Will people be hurt? No. The child is a capable climber and has been taught how to check their footing. I am with the child and can remind them of safety and be a backup. The child is wearing clothing allowing for free movement and quality footwear.
Will the property be hurt? No. This is a steady tree in a public area. The child is wearing play clothes.
Is this bad manners for the situation? Nope. This is a public park, not private property or an event where it would be rude to act out.