If the neighbour doesn't care, then I am sure they would not mind having their property returned to them, over the garden fence? (The poo, not the cats) ;-)
They won't be able to solve that little mystery (assuming poo in their garden bothers them) until they invest in a litter tray... which is only practical if kept indoors.
Beyond that side of it, I hope you manage to witness how the cats are managing to jump onto the bird table. Either it's not tall enough or it's too close to some other garden feature which they're jumping from.
It would be a real shame to have to stop feeding your birds for however long it would take for these cats to get bored of having nothing to chase and move on to someone else's garden, so I hope an amicable solution is found soon.