If you have an insect problem in your garden, stop feeding the birds with bird feeders during the growing season. Ask your neighbors to do the same. We need birds to do what birds do naturally every day…hunt for food. And, we want a large portion of that food to be insects. You are doing your bug infested garden no good if you are intentionally drawing most major insect predators away from it.
For an insect infested garden, we need hungry birds and as long as they have a steady supply of bird feeders to eat from, why go after the insects. In a world without humans, there are no bird feeders, there are only natural food supplies.
Now granted, there are good and bad insects and birds are not discriminatory. But, there are always far more bad insects than good ones. That’s the nature of the predator vs prey world. Predators tend to gravitate towards the largest area of food sources. A large population (bad bugs) will be more attractive than a small one (good bugs).
Also, stop killing, and start encouraging spiders, praying mantises, wasps, and other predatory insects. They are the best defense against bad bugs. It’s called integrated pest management or, letting nature take care of its own.
This should be a seasonal thing. In the winter months, there are no insect problems and the birds could probably use a little help since we humans have wiped out most of their natural habitats and food supplies. At this time, put out the bird feeders.
If we stop feeding the birds during the growing seasons of the year, they will find other sources of food, including your garden damaging bug population.