This is an incredibly divisive issue, so I want to make it clear that I am only giving my personal opinion, and that I do not speak for anyone else. I’m a veterinarian with a special interest in exotics medicine, and I’ve been keep leopard geckos for 20 years. It is my opinion that animals that are closely related should never be bred together.
To my mind, there’s one possible exception. If you genuinely discover a brand-new morph that has never been seen, a very small amount of inbreeding is acceptable initially (and only initially). You have to have enough animals that carry a trait to work with to make it viable.
In a hobby where it’s become everyday to see animals with ocular problems, kinked spines and tails, (potentially) morph-related neoplasia, and neurologic problems, it seems really, really obvious to me that inbreeding is bad. In the past, as a vet, I’ve dealt with plenty of defensive reptile breeders that insist that I don’t know what I’m talking about, or provide some sort of ‘evidence’ that I’m wrong, and every time it’s hard not to laugh. I mean, of course incest = bad. It doesn’t matter if you whitewash it and call it ‘line breeding,’ it’s still going to lead to lowered fitness levels overall and a higher rate of congenital defects.
If you insist on inbreeding, there are statistics you can look up that quantify just how bad each pairing between related individuals would be (like siblings versus parent * offspring, etc.), but to be honest, I don’t know them, because it would be unethical for me to say anything other than ‘don’t inbreed.’ I could lose my license for anything else.