The text is pretty clear on this point:
“She had seen enough of Robert Baratheon at Winterfell to know that the king did not regard Joffrey with any great warmth. If the boy was truly Jaime’s seed, Robert would have put him to death along with his mother, and few would have condemned him. Bastards were common enough, but incest was a monstrous sin to both old gods and new, and the children of such wickedness were named abominations in sept and godswood alike. The dragon kings had wed brother to sister, but they were the blood of old Valyria where such practices had been common, and like their dragons the Targaryens answered to neither gods nor men.” (emphasis mine)
Catelyn IV, ACOK
So I’d question whether Westeros is “a society accustomed to royal incest.” What they were accustomed to was treating the Targaryens as an exception to the role – although not without some sotto voce disgust (see Dunk’s reaction to Egg talking about his sisters in Sworn Sword) – and even that came after A. the Revolt of the Faithful, and B. the Targaryens marrying into other major families after the loss of the dragons, so as to reduce the frequency of incest.
Ned is positioned in AGOT as an exception to the rule – due to the traumatic loss of his family in Robert’s Rebellion and his unusual commitment to his code of honor – which we can see in the Small Council “debate” over assassinating a pregnant teenager where only he and noted idealist Barristan Selmy express a moral objection.