Honestly, I do feel Cilla was demanding too much. Not only do I feel people should be allowed to BBQ, burn wood, have their kids play basketball, and yes even smoke in their own backyard but they should be able to do so without being harassed.
Now is it possible they were doing it "Deliberately"? Sure, that is always possible, but I have also know people believe others are doing something deliberately or on purpose when really it was them simply going about their normal day.
I mean at most, I could see Cilla requesting they BBQ only on certain days. Like the weekend or another day, maybe with the request her neighbors let her know if they have something coming up on a different day, that way she can make sure to be away from the house.
Apart from that though, even if she is vegan, her neighbors can't be forced to stop barbecuing in their background completely nor should she be able to demand the kids can't play basketball. Compromising perhaps, but otherwise it is their backyard.