It's all in how you apply the bird netting. If it's the right netting and it's installed correctly, it works great. I had great success with the netting Dave linked to (sold through Amigoni Vineyards) until some very tiny birds in my location figured out they could squeeze through the mesh. Now Amigoni sells a smaller, pale green netting which has openings small enough to exclude all birds and even the green fig beetles (aka green June beetles). The openings are so small that only tiny snakes or lieards could conceivably become trapped in it, so I'm planning to order a roll and put it to work.
It works best if it's supported by a framework (PVC works nicely) so it's not in direct contact with your tree, and it should be stretched enough to take up any slack, so it doesn't hang in limp folds where birds and other critters can get tangled up in it.