Up until fairly recently, cousin marriages were quite common in many levels of socity, though nowadays its mostly remembered as a royal practice. Some U.S. states have laws against first-cousin pairings, others don’t. It’s still common practice in many other countries.
Inbreeding was prevalent among almost all the royal dynasties I’m familiar with – European, Hellenistic, Roman, etc. This was for a variety of reasons. One had to marry within one’s own class, and the pool of eligible princesses and princes of the right breeding and religion was small. After a few generations every royal family in Europe was related, and marrying outside that limited gene pool was nearly impossible. Dynastic and political forces often matched young people with very close relatives, up to and including first cousins, double first cousins, uncles, aunts, nieces, and nephews.
In the Hellenistic dynasties, as well as the ancient Egyptian and several Asian dynasties, even more extreme incest was practiced. Sibling pairings, father/daughter, mother/son, you name it. This was partly because an unmarried princess was a political danger – were she to marry an outsider, their children would have a claim to the throne and civil war could erupt. Kings would often marry their sisters to keep them “off the market” as sexual agents.
Take the example of Demetrios I, King of Syria. His sister, Laodike, had married King Perseus of Macedon, but returned to him as a widow a few years later. He tried to find her a husband, but her political connections made her an unattractive prospect. Finally Demetrios married Laodike himself in 161, and had three sons by her.
The genealogies of the later Seleukid and Ptolemaic monarchs was a tangled and confusing web of incest – for instance, the famous Cleopatra’s mother and father were uncle and niece; her paternal grandparents were siblings, and her maternal grandparents were also uncle and niece. Her maternal grandfather, Ptolemy X, was a brother of her paternal grandparents Ptolemy IX and Kleopatra IV, and her maternal grandmother, Berenike III, was a daughter of Ptolemy IX and his second sister-wife, Kleopatra V Selene. Gets very confusing.