> (This used to happen in Europe, but during the middle ages the church banned cousin marriages for political reasons: it stopped the nobility consolidating too much power.)
Not so much banned it, as restricted it: dispensations were fairly common among the nobility and royalty, who could afford the fees charged by the Church for the privilege.
And not just cousin marriage, either: marriages between uncle and niece were hardly unknown. For an example somewhat after the Middle Ages, have a look at the family tree of Charles II of Spain [0]: his father and mother were uncle and niece, as were his paternal great-grandparents and his maternal great-great-grandparents. He was descended in 14 different ways from Philip I and Joanna of Castile, at a remove of five, six or seven generations. Of his 16 great-great-great-grandmothers, Anna of Bohemia and Hungary was four of them (and also four of his 32 great-great-great-great-grandmothers). And so on.
Royalty are special and weird, and a drop in the bucket. Overall the ban was pretty successful, it created a world where a few Hapsburgs behaved this way, instead of every guy in a village with three cows to his name.
Their family trees are weird and alien to us because we live in this new world. Whereas I don't think many of his subjects thought that Saddam Hussein's family tree was freak-show material.
I remember reading that the Church in the middle ages was pitted against tribalism. So they tried to make rules to weaken it. One of those was recognizing free consent to marry over betrothals arranged by their families.
Not so much banned it, as restricted it: dispensations were fairly common among the nobility and royalty, who could afford the fees charged by the Church for the privilege.
And not just cousin marriage, either: marriages between uncle and niece were hardly unknown. For an example somewhat after the Middle Ages, have a look at the family tree of Charles II of Spain [0]: his father and mother were uncle and niece, as were his paternal great-grandparents and his maternal great-great-grandparents. He was descended in 14 different ways from Philip I and Joanna of Castile, at a remove of five, six or seven generations. Of his 16 great-great-great-grandmothers, Anna of Bohemia and Hungary was four of them (and also four of his 32 great-great-great-great-grandmothers). And so on.
[0] https://en.wikipedia.org/wiki/Charles_II_of_Spain#Ancestry