In addressing this subject it is difficult to separate fact from the sensational and the situation would appear to become even more difficult in the future.
As long as I can remember, I have been aware of a restriction concerning marriage between first cousins, that is, people who share a common grandparent. As far as I was aware, the restriction did not extend one step further to include second cousins or those who shared a common great-grandparent. As I got interested in genealogy, I came to realize that my own parents were second cousins. In addition, my great-grandfather had two wives who were cousins, so his two sets of children were not only half-siblings but also cousins. The common belief about such marriages was that the unions would produce genetic problems in the offspring, a fact that is beginning to be examined by actual scientific evidence. For example, here is a statement on the subject by the National Genetics and Genomics Education Centre of the National School of Healthcare Science in the United Kingdom:
Cousin marriageEstimates worldwide concerning cousin marriages are difficult to obtain, but in many cultures, despite the risks, such unions are not only permitted but encouraged.
For every non-consanguineous couple there is a 1 in 40 (2.5%) chance that each child will suffer a severe problem, such as a congenital malformation or learning disabilities. A consanguineous couple is at increased risk for both autosomal recessive disorders and several congenital malformations, this increased risk being due to a common mutation in an autosomal recessive gene from a shared ancestor. For a couple who are first cousins in a family where there is no other consanguinity, their overall risk is about 1 in 20 (5%). This risk is therefore double that of the general population. The additional risk for second cousins is 1% (overall risk 3.5%). If there have been several other cousin marriages in the family, the risk may reach 1 in 10 and the risks may need to be calculated from the degree of relationship. If someone in the family is already known to have an autosomal recessive disorder, then risks for this disorder can be accurately calculated. It is sensible to offer carrier testing for autosomal recessive traits known to be common in the couple's particular ethnic group (for example cystic fibrosis in Northern Europeans, Tay-Sachs disease in Ashkenazi Jews, thalassaemia in people from the Mediterranean, the Middle East, South-East Asian and the Indian sub-continent and sickle cell disease in people from Africa, the Caribbean, the Eastern Mediterranean, Middle East and Asia). Couples should also be offered detailed ultrasound scanning in pregnancy, in addition to routine antenatal care.
One practical effect of such marriages on a family's pedigree is the phenomena of "pedigree collapse." I have written about this previously, but not from the point of view of which marriages are allow or disallowed in a particular culture. The issue of permitted marriages is so wrapped up in traditions that it is almost impossible to find objective discussions on the subject.
The New York Times published an infographic showing the laws for or against first cousin marriages here. Throughout the United States, with the decision of the Supreme Court in Obergefell v. Hodges, the whole issue has reached an entirely new level of examination.
From the standpoint of genealogical research, knowledge of the laws, both civil and ecclesiastical, concerning marriage patterns in a community may help solve some very difficult questions. There are so many articles and books on this subject that listing even a few is an overwhelming challenge. I suggest focusing on a particular time period and location for establishing any historical context.