my neighbour has lost the plot
speaking from experience;
By "lost the plot", I don't mean to dismiss the issue as irrelevant - just that their requests have become more and more unreasonable and detached from reality.
I'm entirely happy to make "reasonable" adjustments to how we keep our dogs (and have done), in response to reasonable requests.
Once the requests went beyond reasonable (ie detached from what our dogs do / don't do, ignoring noise from other dogs, times of day & duration etc) and progressed to harrassing mrs rkk01, my inclination to respond in a "reasonable" and neighbourly manner was somewhat diminshed.
The advice from a friend in "law enforcement" was to tell the neighbours to **** off - oone that I haven't yet bothered with, as I still like to try and have the high ground
ETA
There is no need for a dog to bark constantly if trained properly.
They don't - they will sometimes bark at the end of the day before we get home. Mainly because lots of other people are getting home, walking their dogs by our house or loitering around our house etc.
They never bark nightimes / unsociable hours, and very rarely resort to barking during the day.
We decided to keep the dogs in to placate the neighbours - reasonable response to an initially reasonable request. Their own dogs bark more than ours FFS... Ironically, these neighbours are two houses away - next door don't have a problem