This seems distantly impossible right now, but for this reason, I predict that any species that survives this kind of "great filter" effect of accidentally messing up their genome long term, will develop a strong taboo against fertility treatments and treatment of genetic diseases.

Like it seems horrible not to help the individual, when we have the technology to; but it's also horrible to hurt your species by selfishly propagating faulty genes. And this seems like the kind of problem cultural taboos are good at solving, and I don't really see any other mechanism by which a species can avoid this filter trap.