Why does anything need to change? It might be very icky to all outside of Westeros, but incest has been a common theme in Game of Thrones, and in the Targaryen family.
Jaime and Cersei Lannister set the tone with their opening-episode fumble and have been one of the central love stories throughout the entire seven seasons. When Jaime was on the road, Cersei shared a bed with her cousin Lancel Lannister. Jaime and Cersei themselves are the result of a marriage of incest - their father Tywin and his first cousin, Joanna Lannister.
Cersei cited the long history of Targaryen incest as she attempted to justify her relationship with Jaime to Ned Stark in season one: "The Targaryens wed brothers and sisters for three hundred years.” King Aerys Targaryen II, the Mad King, married his own sister, Queen Rhaella Targaryen, making Jon’s Snow’s father Rhaegar, and Dany herself, products of incest.
Basically, anyone who’s anyone in Game of Thrones has got down and dirty with a family member at one point, so why should the dragon and the wolf concern themselves with the opinions of the sheep?