It's important to remember that, yes, inbreeding can show up undesirable recessive genes but one of your birds needs to have that undesirable gene to start with.
Inbreeding is a good way to get rid of the undesirable genes, through culling. This is how show birds (and dogs, cats, horses, whatever) are bred.
Adding 'new blood' may introduce undesirable genes that none of your birds currently carry and then inbreeding can increase it's presentation in your birds.
Depending on what you want to do with your birds (if you are just collecting eggs), inbreeding is unlikley to cause major problems. You should monitor their progress, if you find egg production is dropping them perhaps you are losing vigour in your flock. If you are breeding for meat then you need to monitor both egg production and fertility. Susceptibility to disease is another. For some, poor egg production and low fertility is OK as long as the few chicks that make it have something desirable, like long tails, good posture, specific coloring.
As you've noticed, chickens are not morally offended by inbreeding and neither are most animals, in fact for some animals it's absolutely the norm.
In either case, in or out breeding, you should not allow poor quality birds (whatever *you* rate quality on) to continue their line.
As mentioned, there are many threads on this subject, they are well worth reading.
