I've read different views on this; first observation is that they nearly all seem to be coming from a 'breeding to the SOP' (standard of perfection for a given breed) perspective, even the >100 year old handbooks; in any case the keeper chooses which birds are going to be allowed to breed.
Second observation is that the number of birds being worked with makes a difference: serious breeders are selecting a handful of birds to breed from out of cohorts of literally hundreds of siblings that were themselves the result of the previous years' decisions about who to mate with whom, and they will be keeping separate strains or clans in separate pens to boot (I think that's called spiral breeding, on which see e.g.
https://www.motherearthnews.com/homesteading-and-livestock/how-to-breed-chickens-zmbz16amzkon/ ). Although they're both a sort of inbreeding, that's completely different from breeding one roo and 3 hens in a backyard pen.
Third observation is that the quality and variety of the foundation stock genetics makes a difference. One of the problems with rare and heritage breeds that I've encountered is the absolutely small gene pool. If the numbers get really small, it's quite hard to find unrelated birds, and if there's a congenital problem, they've likely all got it. It can be a similar situation if someone starts with birds of the same breed from the same source, as many of us do when we get into chicken-keeping; they're probably already closely related, especially if that source was another backyard keeper with a small flock of X, and not a professional breeder running multiple strains.
For myself, I have come to trust my flock's instincts, in breeding as in brooding and feeding. They mate as they wish. I still have and exercise control over which and how many hens' eggs to set when there's a broody (at least until one of them manages to hide a nest and disappear, only to return with chicks in tow, which may happen one day), and then spend many happy hours trying to work out, as they develop and feather out, each chick's parentage. Sometimes I revise the putative lines so many times I'm not sure why I bother

That they are healthy is all that really matters here.