Wearing a bike helmet limits injuries to cyclists when they are involved in accidents, but in no way does not wearing a helmet cause accidents. However, pedestrians, motorists, and other cyclists who yell at passing bicyclists for not wearing a helmet can cause accidents.
A lot can happen in the second or two a cyclist is distracted from watching the road — a car door can swing open, a child can run out into the street between two parked cars. If you disapprove of cyclists not wearing helmets, bring it up in conversation or write to local politicians to push for a helmet law. But when you see these cyclists in the street, keep it to yourself.