Incest is taboo in Westeros -- to an extent
For the most part, incest is frowned upon in the Seven Kingdoms. In fact, according to George R.R. Martin's source material, it's considered a cardinal sin, along with kinslaying and violating guest rights – a taboo trifecta the Lannisters had no trouble clearing. The arrival of Aegon the Conquerer, who invaded Westeros and established the Targaryen dynasty, challenged religious views on the practice when he took the crown. (In addition to incest, Aegon also practiced polygamy: he was married to his two sisters.)
Soon after Aegon's death, the Faith Militant tried to banish the Targaryen habit of intermarriage -- which they maintained in an effort to "keep bloodlines pure" -- but were unsuccessful. Incest was still widely seen as an abomination, but the Targaryens were considered a royal exception.
When the Targaryens were defeated during Robert's Rebellion, incest was once again outlawed. However, something important to note is that cousin marriages weren't considered illegal in Westeros and were, in fact, a fairly standard practice. Jaime and Cersei's parents, Tywin and Joanna, were first cousins, and Ned Stark's parents were first cousins once removed. That means both of Jon's assumed parents – Lyanna Stark and Rhaegar – were the product of incest to varying degrees.
So, assuming Jon and Dany get together, does the cousin thing mean their relationship might escape taboo? Not quite. Avunculate marriage – or, marriage between aunt-nephew or uncle-niece – is as frowned upon as brother-sister unions, due to a higher percentage of shared DNA than that of first cousins. This probably wouldn't bother Daenerys – in the books, she assumes she'd have married either her brother Viserys or her nephew Aegon had circumstances been different, and grew up with the knowledge of her Targaryen heritage. Jon, on the other hand, was raised by the Starks of Winterfell, who worshipped the anti-incest Old Gods. He'll almost certainly have an aversion to bedding his aunt, unless the apocalyptic threat of the White Walkers rewires his Northern dignity.
Of course, the new world order in Westeros has superseded established norms. Jon, a bastard, was named King of the North, after all. Maybe with the looming White Walker threat, an aunt-nephew romance is a low-priority problem.