Inter breeding closely related genomes will result in two things. It reduces or eliminates genetic abnormalities and it reinforces or increases those desirable attributes. This practice is used by cattle breeders all the time, as well by many other domestic animal breeders. The animal breeders then cull the abnormal ones thereby improving the breed.
Those cultures that engage in marrying brother to sister or first cousin to first cousin fail to cull the abnormal resulting in a decline of the affected population. The decline when it is first cousin marrying first cousin is very slow and probably not noted until modern day.
Let us keep in mind, where do we draw a line? After first cousins, after second, fifth, twentieth? It is a near certainty that all of those of European heritage are cousins and probably over 60% that the entire world population, seven billion, are cousins. There is no such thing as a perfect stranger among the human species.
In fact, many of them were not even vertebrates.
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It not just marrying cousins, it’s continuing this practice for generations, even hundreds of years. In these groups, members would be as genetically close as siblings, or even closer, if possible.