I know how you feel, my neighbour made a fuss over me locking the gate, fire hazard was her excuse. None of the others objected. I have a yale lock on the inside so its not a fire hazard at all. Later because it was left open a robbery occured outside my garden. She had private long fencing and a private gate so she was alright. I would go out every single night and make sure it was locked properly. I have done this for 7 years. You could try to offer discussions on the yale lock option but I doubt it would work. Seems like difficult neighbours to me.
0r better if they had something happen to their property or garden through the back entrance I am sure they would think twice. I know I am bad (lol). O.k don't listen to me I will only get you in trouble. I meant someone else do it. don't rise to it yourself this is exactly what they want.
You could offer to take there bins out once a fortnight, but I dont think you should. You can't win with this type of people. I would prefer to move but maybe thats what they want.