GRRM said several times that his inspiration for ASOIAF was the War of the Roses. Well, apart from Edward IV (who married a commoner, making a real scandal), all the Yorks married their COUSINS at the very least (some were first cousins) . All they needed was a dispensation from the Pope, who was at the time quite busy signing the many royal requests throughout the Christendom.
King Richard III was rumored to have bedded his niece, the daughter of his brother King Edward IV. The rumors were so strong that he was forced to make a humiliating public statement to deny the rumours. His own wife, a cousin once removed, was not even one month in her grave.
It was common among the aristocracy in the middle age until recent times to marry in-house to mantain the privileges, lands, properties and titles.
Incest as forbidden practice, dictated by the Bible, was formally allowed by the Head of the Church with a special dispensation.