Here is one version of it:
There are some problems with the rhetoric.
The dog example is probably the worst offender.
"At the same time, humans are perfectly comfortable with the idea that inbreeding can produce genetic benefits for domesticated animals. When we want a dog with the points to take Best in Show at Madison Square Garden, we often get it by taking individuals displaying the desired traits and "breeding them back" with their close kin."
You fly that one past a few dog owners and see how _they_ feel about animal breeders using this tactic. You'll find some fraction that is a-o-good with it -- and you'll get a couple earfuls from a lot of the rest. Dog breeder choices are _not_ regarded as good ones from a population health perspective.
"for generations the Rothschild family had been inbreeding almost as intensively as European royalty, without apparent ill effect."
That is a family that is fully capable of keeping its secrets. Absence of evidence is not evidence of absence.
"So when a team of scientists led by Robin L. Bennett, a genetic counselor at the University of Washington and the president of the National Society of Genetic Counselors, announced that cousin marriages are not significantly riskier than any other marriage, it made the front page of The New York Times. The study, published in the Journal of Genetic Counseling last year, determined that children of first cousins face about a 2 to 3 percent higher risk of birth defects than the population at large."
This is ambiguously worded. If the population has a risk of 1%, does a 2-3% increase mean just a shade over 1% or does it mean 3-4%? A little googling provides:
"they estimate the additional risk to range from 1.7 to 2.8 percent for first cousin unions"
This can be presented as 2-3%, as Discover did, but if you wanted to scare the crap out of someone, you could equally say that cousin marriage doubles or triples the risk (if the gen pop risk was 1% -- if the gen pop risk was <1%, you could say something even more terrifying). Most commentary about risks aimed at women contemplating having a baby is presented in scare-the-crap-out-of-them mode. I can't imagine why this situation should be treated as somehow special.
Robin Bennett is absolutely _right_ about her experience as a counselor. When someone is sitting in that room having The Conversation, they _definitely_ think the risk is worse than it is. They always do. I would not, however, suggest being entirely dismissive. Further, this was a meta-study (appropriate for counselors) and the data was thin on the ground and not tremendously relevant to the gen pop anyway.
The wikipedia entry on cousin marriage (there is one) has some interesting tidbits stashed away in it.
In fact, there are other articles on the topic as well:
My sister (who worries a lot about consanguinity) is a nurse who works with children with special needs. She's been talking about some of these issues in particular populations (let's just call them related to the group of people described as living in the town of Bradford in the Discover article above, but obviously not in Bradford); I always tend to suspect that the story is a lot more complicated than she thinks it is. It would appear that genetic counselors from Bennett to the Middle East all think that the problem is not cousin marriage, but rather inadequate testing and counseling. Make of that what you will.
There would appear to be two forces at work here (at least). On the one hand, in a large population with low rates of 1st or 2nd cousin marriages (on the order of 1-2%), a particular family can probably get away with a century or perhaps 2 of organized marry-your-cousin-please. That is, they can successfully conceal most of the ill effects against the background noise of health problems in the general population. A particular couple can do whatever the heck they want and you'll only notice it if you study them as part of a class of people doing exactly the same thing. On the other hand, in a population with high rates of 1st or 2nd cousin marriages (on the order of a third to half or more marriages between 1st or 2nd cousins), everyone should be tested for the group's known genetic problems prior to deciding whether to marry, and probably do some testing per pregnancy and also after the each child is born. (This would appear to be the direction that policy is going in the Middle East.) That's called "mitigation".
It's really obvious, looking at all this, why large populations that have administrative continuity (the Hindi, the Han, the leftovers of the Roman Empire in the form of the Catholic Church) apply so much pressure _against_ cousin marriages, but are then willing to allow exceptions. That's not hypocrisy or stupidity or ossified useless rules or anything. That's _exactly_ the right social policy.