The modern consensus is that cousin marriage is 'a bad thing' because of the higher probability of genetic disease among close-ish relative.
Cultures which practice cousin marriage certainly experience much higher rates of genetic disorders - especially those relating to rare and recessive genes. The clinical genetics wards in the UK are very obviously populated by the offspring of such cultures.
But, in the conditions of historical human selection, this doesn't matter.
Before about 1800, all human societies experienced very high rates of child mortality (probably about 2/3 or 3/4 of children died before maturity) - so most babies that were born would not have survived until adulthood.
Any significantly deleterious gene combinations resulting from relatedness would be eliminated by this harsh selective sieve.
So a somewhat higher rate of genetic diseases would barely be noticeable, and easily outweighed by the group benefits and social advantages which cousin marriages might be expected to bring.