YABU (in some instances
)
We have one for DS. He is only allowed to play on it when I am keeping an eye on him and wouldn't dream of letting him screech and yell in the garden, regardless of having a trampoline. It's only a six foot one and his jumps only get to be about a foot high. I probably wouldn't have a bigger one and am strict about only one child on at a time.
I'm sure that some people let their children out at all hours and I can see why that would be irritating but I think they'd do that whether they had the trampoline or not! As for having it one foot below the level of a fence or letting your children hanging over the top of a fence is incredibly rude. I feel sorry for all of you, some neighbours do not get how people like their gardens to be private spaces.
DrinkSangria not sure if you were joking, but to say it's the sort of people who have loud BBQs and play music is a bit of an over generalisation! We're quite the opposite. I hate that the neighbours play music in their garden and their daughter is screeching and bothering me all day long when I'm out there. They don't have a trampoline FWIW.
As for privacy, on the side the trampoline is they haven't done anything about the disgusting chain link fence. No arguments about privacy from them, strangely enough!