What a "line" really is is a family that consistently produces offspring within a narrow range of variability. For people who show animals, this is desirable, because, in essence, you "know" what's going on genetically and can make predictive matings. What happens is that in outbred animals, there is a great deal of heterozygosity -- in other words, there are a lot of genes that are had as two different versions in the same organism. The dominant version will show in the phenotype, and the recessive version will remain hidden. With outbreeding, the chances that an unrelated individual will have the same hidden recessives is less than with related individuals. So the negative effects of those recessive genes being expressed (and thus being had homozygously) would be prevented by random outbreeding versus inbreeding. However.....
If you wish to establish a new line, you start with a few individuals that have characteristics you desire. By inbreeding their offspring, you will find a lot of individuals early on that express those hidden recessive traits. These are purged from the breeding population (i.e. culled). You keep only those which continue to possess the desired traits in the parents. By switching around the partners, you can find out which pairings give more desirable offspring than others. What this does is indirectly tell you which individuals do not carry a negative recessive trait (remember, for each trait that is heterozygous in the parents, 1/4 will be homozygous without the trait...if you find two homozygous birds without the trait and breed them, none of their offspring will have the negative trait that was carried in by the original unrelated parents). When you get to this point after enough generations, you are producing cookie-cutter offspring that are nearly clones. In other words, there are no longer any hidden recessive genes -- what you see is what you get. From this point on, inbreeding won't really matter much -- except to say that without variation within the population, you'll have to be vigilant about preventing new diseases from getting at your flock. This is why people who begin with an already established line can continue to inbreed without seeing negative effects -- a lot of hard work was already done by the originator of the line to get to that point.
So when someone asks "is it ok to inbreed?" I'd answer "well, what are your goals?" If you want to produce cookie-cutter animals to match the breed's SOP or to produce uniform food, then inbreeding to start a line is probably the way to go. Be prepared, when beginning your own line (not getting animals from another line and continuing it, but starting your own from unrelated individuals) to cull heavily in the first few generations to purge harmful recessives as much as possible. If you keep your animals free-range, be aware that parasites continue to evolve, and with a group of animals with very little variation, it's possible that eventually a disease could decimate the flock. If you want to maintain a population for your own consumption and don't have the resources to raise lots of animals and cull 90% for the first few generations, then a healthy amount of genetic variation would probably suit you better.
P.S. I'm basing my information on some research I've been doing on the origins of inbred lines of mice used in laboratories, and applying those principles to livestock.