Will garden birds stop using my feeder if my neighbour has just put up a new feeder?

Hi Kaie, I am sure that the birds will investigate the new feeders next door to see what is on offer, but also I am sure that they will keep coming to yours. If you have bird seed out you could offer something different, sunflower hearts, they love them and Niger seed. You will get finches and Siskins taking them, maybe try making some home made pastry. Very simple to make, shops own brand flour and fat, mix half the fat to flour, as you would for human pastry. Mix into that seeds, crushed nuts (especially just now when there are young birds about) sunflower hearts, grated cheese, surt pieces, dried fruit (sultanas, raisins). Mix that with a small drop of water, enough to to bind it and keep in the fridge for a few hours. You can then pull of pieces and put them into a peanut type feeder, or empty coconut shell (if you have one) or make your own out of an old yoghurt pot and string. You could also pull of small pieces and squeeze them round the tree branches, or in the joints on branches. They love this, but beware once the find it, they will be back. That may keep them in your garden!