For a long time, businesses that cross animals that are closely related to each other have existed with marked disapproval from society. For this reason, many ranchers are afraid to breed any animals that were even born on the same farm. But that really doesn't make any sense. The way breeds and lines of livestock are formed is by one ranch dedicating itself to producing quality animals with certain characteristics. When they reach uniformity in their herd, through linebreeding, they title their livestock as a line or breed. Often the way they get uniformity within the breed or line is by breeding animals that have strictly been raised on their ranch so they are certain that the genetics will be sound. Then they will occasionaly outcross their bucks every few generations to stir the genetic pool a little. So how is creating a line or breed of livestock any different than inbreeding? The lines get kinda fuzzy here.
To many people, inbreeding would be classified as breeding any animals that have ever shared common ancestors. I'm sorry, but with that criteria, you just can't breed animals. Every animal in every species will have some ancestor from 4000 years ago that was also related to the one you want to breed. A more reasonable and widely accepted view is that, as long as you don't breed close relatives (like parents, cousins, uncles, etc.) then your probably doing alright. According to Sue Ann Bowling, "inbreeding at its most restrictive applies to what would be considered unquestioned incest in human beings - parent to offspring or a mating between full siblings. Uncle-niece, aunt-nephew, half sibling matings, and first cousin matings are called inbreeding by some people and linebreeding by others."
For more in-depth information from Sue Ann's website, click this link to her very informative article about inbreeding and linebreeding in dogs. While it's not the same species as goats, there is a lot of good information to read and think about.