Prolonged interbreeding in any species can eventually lead to serious birth defects. Harmful genetic mutations are less likely to appear in large populations where individuals reproduce with random partners due to the wider variety of genetic mutations.
But in small, isolated populations where inbreeding is common, there’s a greater chance that related partners carry the same mutations.
However, harmful effects are more common in groups with a history of interbreeding over several generations.
First cousins that are not from such groups run only a slightly greater risk of producing children with birth defects than non-related couples.
Although such risks should not be ignored, first cousin marriage is not necessarily a recipe for genetic disaster.