There are a slew of reasons why closely related people should not marry, but birth defects really aren’t one of them.
Unless there is a dna history of undesirable recessives, the risks to their kids is no greater than any two other people.
Except when it’s been SOP for dozens of generations, concentrating a lot of poor quality recessives.
You are correct that one generation of cousin marriage is not a problem. But Muslims keep up the cousin marriage for MANY generation, until it is basically sibling marriage.
My grandfather's brother married his first cousin once removed (in Europe, not the US) and they had five children. One died at birth but the other four had long lives. Only one of them married and she had no biological children (she adopted the son of her husband, whose first wife had died).
My grandparents on one side seem to have been third cousins once removed. I think that is distant enough not to be a cause for concern.