The matter of pursuing the Throne was always an underlying issue between some players, but Dayne's first appearance kicked everything up to the surface, and the subsequent debate was... extreme.
The Waifu Wars. All the players have their own view on who is the best girl for Jon to marry, with the main contenders being Desmera Redwyne, Cerenna Lannister, Margaery Tyrell, Meera Reed, and Roslin Rosby (formerly Frey).
Upon the results of a contentious vote that saw Bran warded at Seagard instead of Harrenhal for being a "Destiny Point sink", a large portion of the playerbase have taken to calling this to mind every time large amounts of Destiny Points are used with the exclamation "DP sink!", which is usually followed by "Forever salty".
"Plan Friendship" became a common mockery after a vote not named according to the rules brought to the loss of twenty two Destiny Points (the sheer amount of vitriol and spite over that vote certainly didn't help either).
Odran/Bizuneh's signature "literally nothing wrong" which earned him two expy characters: Hugor of the Hill and Odran zo Odran.
Jon being worse than Littlefinger, said by several voters who left following the defeat of the infamous Plan Friendship.
Moral Event Horizon: Some players felt that Jon had passed this after the betrayal of Tyrion's trust in order to place Dana Wells as High Septon and left the quest.
Doubly subverted with Arthur Dayne, who the players had good reason to suspect and did actually end up betraying them, but managed to escape suspicion for the entirety of his on-screen appearance for most players. The same happened with Loren Lantell and Hugor of the Hill.
Sturm Brightblade. The sole survivor of several Crimson Sept attacks whose family had ancient ties to the Faith Militant. Only it took two Arryns dying for anyone to expect him.
Paranoia Fuel: The very existence of the Crimson Sept is this. Every candidate for High Septon has been suspected, as well as virtually every named character in the Vale.