Inbreeding in the real world only affects the inbred baby if the genes that the parents carrry have less than 12% genetic difference. If the difference is above that, there won't be much complications over-all factors considered. Unless the dominant gene taken from both parents are the "bad" gene, having a higher than 12% genetic difference won't harm the child.
It's a misconception that if cousins or siblings have children, their offspring will immediately be genetically disabled. This is false. There is a higher chance with siblings, but not if the siblings were from parents of different family trees. This is because there is a high possibility that the genetic mark-up of both children did not come from just one of the parents but both of them, rendering them a high chance to have genetic differences enough to create an offspring that functions as normally as possible.
The only sure way to have genetically problematic offsprings is when the inbreeding happens in more than one, and I can even push to the next two generations. The second inbreeding level is harmful enough to the child, but the more the practice is continued, the higher the chances of negative effects.
In rabbits for example, parents breeding with their offspring will not affect the babies as they bear quite the genetic difference. Sibling breeding, most especially from the same litter since their genes are very similar from each other, is highly discourage as there is a high risk of having genetic anomalies such as decreased resistance to sicknesses and infections, bone structure defficiencies and over-all function. This is, though, not a 100% case and most often than not, they may produce functioning kittens. Though, breeding from parents and litter of these third generation kittens are highly discouraged due to the shared genetic markup of these babies with their parents. Breeding them to their grandparents may have varied, but more positive results.
I've bred rabbits before (though I segregate the females and males as to prevent such accidents) and have researched a lot. Haha!
Remember, DNA contains so much genetic data and 12% difference is a very small percentage. To reach that level, it will definitely take generations for the effects to kick in.
It's also a high misconception that dogs and cats are inbred to create the perfect babies. It is true that there were a lot of inbreeding, but they brought in fresh blood that resembled the genetic preference from time to time. Most often than not, they had three branches prepared as it is a planned thing, not on a whim. The inbreeding happens when the breed starts to become commercial and there are breeders that are interested, but aren't careful. Usually, the foundation of the breed is not inbred, it only comes later on and doesn't bear extreme effects due to how DNA works.
Of course this does not apply to all breeds and there are definitely certain breeds that started as an inbreeding result, but most breeders that want to breed for certain traits, especially in our time, do not result to inbreeding anymore as the issue has gotten out of hand. Breeders that inbreed do it not because of desparation or because there is no genepool/external sources, but because of commercial and money generating purposes. It's why even if the offspring is normally functioning, if it is inbred, it has a negative feedback because of the abuse most commercial breeders do.
