Children of first-cousin marriages may have an increased risk of genetic disorders, particularly if their parents both carry a harmful recessive mutation, but this can only be estimated empirically, and those estimates are likely to be specific to particular populations in specific environments.
As if there weren't enough incest threads on this board already ...
Specifically, until the 1860s or so, first cousins commonly married in Europe and the U. Nonetheless, the practice soon fell out of fashion in the United States.
Although never outlawed in England, during the second half of the 19 century, many states began to ban marriages between first cousins, as part of a larger movement after the Civil War for greater state involvement in a variety of areas, including education, health and safety.
Cousin marriage is common in the Middle East, for instance, where it accounts for over half of all marriages in some countries.
In some countries outside that region, it is uncommon but still legal.
I'm not sure how that would influence attitudes in the rest of the population - seems to me it could go either way. Getting to the nub of the OP, as a Brit, I feel the general attitude would be a raised eyebrow and probably snide jokes about Deliverance but not disgust or shock.
So let's imagine a couple in the UK, first cousins, in a serious relationship, of age, male/female, fertile, from a family in which such a relationship has not occurred in some time and not part of an immigrant culture in which such relationships are commonplace. I don't think it is common in the majority of the population, perhaps Chronos' novels were about the aristocracy?
Banning Cousin Marriages While there have been instances of the banning of marriage between cousins at various points through history, such as the Roman Catholics banning the practice for a time starting with the Council of Agde in 506 AD, for the most part marriage among cousins has been popular as long as people have been getting married.
As Frame Game has argued before, topics such as sex with animals, dog-eating, and sex with cousins are never as simple as they're made out to be.
You can't just say the practice in question is icky.
Researchers note that the distinction in marriage bans between England and the U. may be explained by the fact that, in the United States, the practice “was associated not with the aristocracy and upper middle class [Queen Victoria and Prince Albert were second cousins] but with much easier targets: immigrants and the rural poor.” Regardless, cousin marriage bans began popping up across the states, with the first in Kansas (1858).
people with common grandparents or people who share other fairly recent ancestors).