There is no doubt that some people suffer from grey squirrel damage and I can appreciate that these people want the squirrels gone. So be it, I have no objections with that.
In the garden at our home we have a healthy wild bird population as well as a family (?) of greys. The greys used to live in a large tree at the side of the road but the new neighbours had the tree removed so the squirrels decamped to a large apple tree in their back garden. We enjoy watching them. There seems to be four of them, one with virtually no tail that we refer to as 'Stumpy'. There is a very large ash tree on the border between us and next door .. the squirrels play on it. They also play in our garden and can be most amusing. Yes, they are a pain at times.. planting walnuts all over the place, digging occasional holes in the lawn but generally we co-exist quite happily. They take food from the bird feeders but so do other so termed pests ... magpies, pigeons etc. We like to think that by eating the food provided for them they will not need to go egg hunting.
Rats are another matter; they are eliminated whenever the opportunity arises.
Cheers, Phil