When the Geese in my local park first had goslings I expected there to be some kind of warning when passing them on the path, but they seem completely unfazed, even when they cross the path in front of you. They currently have goslings of widely varying ages and still seem the same.
That said the swans seem quite laid back too - I don't feel it is reasonable to approach them closely, but I have seen the parents accepting food while accompanied by their cygnets.