Pigeon "dispute" with neighbour

Hi all, It seems other people have experienced a similar issue, but we have had a complaint from our next door neighbour about pigeons. In fact without discussing it at all with us, we just received a letter from the council warning us about "persistent pigeon feeding". It also seems that he reported rats in our garden, which is a blatant lie as we have two cats, who while rather too fat and lazy to bother the birds, are certainly discouraging to rats and mice. We have been feeding birds (and squirrels and hedgehogs) at this house for nearly 10 years in the same way, just couple of hanging feeders and a couple of small open trays, plus a tray of nuts some distance away to keep the squirrels busy. Of course we have always had a few pigeons, but this year we have seen a lot more for some reason, however we wanted to keep feeding as we knew other local birds were fledglings and many of these young birds were coming to our table as well. Having got the letter I approached the neighbour about it and offered to order some caged feeders and other bits to 'pigeon proof' our feeders. I have no problem with this as the pigeons do poo a lot and I understand they can be a pest to some people, and tend to scare off the smaller birds. There is, I note , no poo on his roof, shed or fence, the birds only come into our garden, so any mess is our problem. However it seems that before he contacted the council the neighbour decided to post pictures of our house and garden featuring said 'pigeon menace' on Facebook publicly, and invited comments from his many ignorant friends who suggested variations on shooting or poisoning the birds, or in more than one case, to "shoot the birds, then the neighbours". Nice people. My wife especially likes to feed the birds as she has MS and is essentially housebound, so the best way to see the wildlife for her is to bring it to our home. I am literally stunned that anyone I know can be so mean, and so uncaring about humans and animals alike. Its got so that my wife is scared to feed the birds in case she is doing something wrong. Anyway, based on the posts on this site, we have contacted the council and will happily allow them to visit our new feeder setup. Despite intimidation, we have no intention of stopping feeding any of the creatures feathered or furry, that come to our garden. Not really looking for advice here, but a bit of "moral support" would be very much appreciated right now...