If you are breeding for meat, sib-sib breeding is fine--you only keep the very best. This is why line breeding is biologically undesirable the higher you get on the food chain:
If your breeders typically have 5-10 (or more, for some species) offspring per breeding, and will have many breedings across their lifetime, line breeding is very acceptable. Particularly if unacceptable offspring are permanently removed from the gene pool, either by surgical sterilization (spay/neuter), or by culling to the freezer. The percentage of unacceptable offspfring is more than compensated for by the sheer number of offspring created.
If your breeders have 1-5 offspring per breeding and will have numerous breedings possible across their lifetimes, the sib-sib breedings may still work out, but more caution is advised--you should be really good at identifying potential negative traits and avoid crosses that might intensify those. The potential is still good that the majority of the offspring will be fantastic valuable members of the gene pool.
If your breeders (like humans) have one or two offspring across their entire lifespan, the potential for deletrious traits is statistically NO HIGHER than with the rapid breeders for each individual offspring. But the cost of a single unhealthy offspring is deemed so catastrophic for the parents, genetically, and in humans also emotionally, that societies have elaborate and non-negotiable taboos against such mating. In some animals like primates, males are driven away from the family group at puberty for this very reason.
It is basically all a function of birthrates. Rabbits are among the high birthrate category for mammals, so line breeding and inbreeding can be acceptably practiced if you are able to recognize negative traits and breed away from them. The rabbits themselves are completely unconcerned.