> If both parents have a recessive gene for a recessive genetic disorder, their offspring will inherit that disorder. That's why people have such an issue with it.

This is simply not accurate. Or rather, it's partially accurate, and it's only part of the story. The increase in risk isn't huge, and the amount it happens effectively leads little to be concerned about.

"Contrary to widely held beliefs and longstanding taboos in America, first cousins can have children together without a great risk of birth defects or genetic disease, scientists are reporting today. They say there is no biological reason to discourage cousins from marrying."

"'In some parts of the world,' the report says, '20 to 60 percent of all marriages are between close biological relatives.'"

"Dr. Motulsky said researchers did not know why marriage between cousins was viewed with such distaste in the United States. He said some of the revulsion might have stemmed from the eugenics movement, which intended to improve the human race by deciding who should be allowed to breed. The movement flourished in this country early in the 20th century." [1]

https://www.nytimes.com/2002/04/04/us/few-risks-seen-to-the-...