Ok, inbreeding, taboo in the human race because of the possibility of less desirable traits being thrown, and the severe possibility of doubling down on genetic disorders. Our ancient ancestors worked this out quite quickly I think. My husband came from one of a group of small islands off of the North of Scotland, and raids to find new women have been going on forever. At the same time there is an upside, you can magnify any good traits, you have a chance of improving the desirable. In the human world we are against such experimentation, because the poor folk who are born carrying the negative traits are too big a price to pay for the chance of positives. Besides there is no breed standard for people.
For the animal world though, it is how new breeds start, you have one desirable animal with the traits you want, then you start inbreeding with close relatives who have those traits, and once you have offspring, then you can breed them back to the parents. Lets stay with the cattle world, in that case the ones that carry the right traits will be bred, the failures either die, or we let them grow then eat them! It is not a venture for the faint of heart, or those without a depth of knowledge of what they are trying to achieve, the risks involved, and the possible costs, emotional, financial, and on the health of the animals. It is a high risk game for all involved.
Line breeding is far more wide spread, but again should be approached with a little caution, and a whole bunch of knowledge. My beautiful Arab, has Bask and Serafix many many times in her pedigree, no inbreeding, but line bred so she has many common ancestors. They certainly produced a mare of great beauty, and she has no health issues, so either she is lucky, or people have cared enough to do their homework and make sure that they made good choices.