I knew two sisters who married their first cousins, two brothers. This was in the 80s and they were white British, not Muslim or Arab or from any other culture where this would be encouraged or considered normal. As far as i know there were no particular hereditary conditions in the family, and they each had three healthy children. Imagine their had been an inherited condition, autism or cystic fibrosis for example, and any of their children had married one another, and any of their children had done the same. This is how birth defects from inbreeding happens. It's how pedigree dogs end up with heart defects or breathing problems. It's how King Charles of Spain ended up with epilepsy, lifelong impotence, low IQ and facial disfigurement ('It was noted that he “swallows all he eats whole, for his nether jaw stands so much out, that his two rows of teeth cannot meet.”)
It has always happened to a small degree, in remote communities where large families were common before birth control was readily available. These days it's generally only in certain Muslim cultures were it's considered a requirement or an expectation, to keep money within the same clan. It's rife in the Arab gulf states.
It's not considered taboo in most societies because in general there is no hugely increased risk to the offspring of consanguineous relationships, so long as it doesn't happen generation upon generation within the same extended family. We recognise that the occasional love marriage that just happens to be between first cousins is not a particular risk to their children, and only becomes so when it's a regular and repeated practice and/or their are known genetic conditions present in both the mother and the father's families.
However, in communities where first cousin marriage does happen down the generations, you end up with a very small gene pool and all the associated problems that go along with that. Genetic anomalies, inherited syndromes, birth defects, life limiting conditions causing LDs, autism, epilepsy, profound physical and mental disabilities, heart defects etc passed on at a greatly increased rate than in babies born of non-familial relationships. Studies of the British Pakistani community where over 50% of marriages have been consanguineous for multiple generations show that the children born in those communities are massively disproportionately more likely to suffer from inherited syndromes, disabilities and birth defects than babies born to non-related parents in the UK in general.
There are other minority communities where this is evident too. In the Irish Traveller community there are disproportionately high incidences of Hurler Syndrome for example, among others. They don't marry their first cousins as a cultural expectation, but as a community where few people 'marry out' and where large families are common, it's easy to end up vaguely related to your spouse.
Any fairly insular minority community is going to experience this to an extent, even if they don't expressly encourage the marriage of first cousins, because the gene pool will be limited compared to the rest of the population in general. But add a culture of first cousin marriage into the mix and it will obviously hugely compound the problem.
Incidences of Sickle Cell Disease are much higher among people of African Caribbean heritage. If both parents have the gene, there's a 1 in 4 chance of each child they have being born with sickle cell disease. The child's parents often will not have sickle cell disease themselves and they're only carriers of the sickle cell trait. As a rule, people of AC heritage do not marry their cousins, but if they did, as a common cultural practice or expectation in the way that many Muslim communities do, you can only imagine how much that would make the prevalence of SSD.
It costs the NHS (by which I mean the taxpayer) an unbelievable amount of money every year to support the poor victims of this highly questionable cultural practice. It makes me furious because it's nothing more than outdated feudal, tribal nonsense that is all keeping control of money, land and assets within one family/clan. It's completely unnecessary and avoidable and these poor kids who suffer the consequences are just collateral damage.