What Happens When Cousins Procreate?

If two cousins procreate will their children actually have a higher risks of birth defects.?
The more DNA you share, the greater the chance your offspring will have a genetic disease — like cystic fibrosis or sickle-cell anemia." Business Insider
That why marrying your first cousin is illegal in 24 US states.
People related to each other are more likely to carry the same genetic diseases.
That's why their children are more likely to have them as well.