It is a myth that if humans contact a baby bird or bird eggs, the parents will abandon the nest. Most nesting birds have a poor sense of smell. (This does not imply that all birds have a bad sense of smell – some birds have incredible senses of smell.)
Birds work very hard to build a nest and lay the eggs. A little human contact is hardly going to make them abandon the nest. Nevertheless, it is in the best interest of the birds to leave the nest alone.
But what do you do if you have to move a birdhouse? First, ask yourself if you absolutely have to move it. The breeding season is not very long. Can you wait until the chicks have left the nest? If the answer is no, then plan to move the nest and its inhabitants in daylight with as little disruption as possible. Have the new location ready to go. Gently remove the birdhouse and move it to its new location, keeping it upright all the while.
The parents will be upset and will make quite a racket. Thus, you should leave the area quickly, and let the parents find the birdhouse in its new location.
After it has moved, watch the birdhouse from a hidden location. Chances are that the parents will find the new location and resume feeding the young or sitting on the eggs. If hours pass, however, and it appears that the parents have abandoned the nest, then you should contact a wildlife rehabilitator in your area to ask for advice.
There is a myth that human contact with a bird will prevent the parents from sitting on the eggs or feeding the young. This is, however, just a myth. According to Bridget Stuchbury, a professor of biology at York University in Toronto, “Parents put so much effort into building nests, incubating eggs and caring for young that they rarely desert nestlings simply because a person has found the nest.”