The Lineages and Histories of the Great Houses of the Seven Kingdoms is the book Jon Arryn asked for and Ned read before he was killed for exposing the twincest. There is no DNA test in Westeros, so aside from Cersei admitting it publicly, which she won’t, then the tapestries are a pictorial version of the Lineages and Histories, which is very important because most of Westeros is an illiterate society.
The literate and illiterate alike can look at the tapestries showing strong black haired, blue eyed Baratheons. One after another. Each with the signature Baratheons black hair and blue eyes. Not a single blonde haired member. Then they will they think about what Tommen and Myrcella look like and scratch their head and think if the rumors really are true.
It is a Westerosi Maury Povitch DNA-tapestry. Robert.. you are not the father.
When the time is right Littlefinger will pull this card in front of his lords to create even more chaos. It is of course, a laddah.
The Riverlords and Northmen hate the Lannisters. Between Petry and Sansa they can control them. With Sansa marrying the LP of The Vale, then we have the Vale coming into the fold to defend their Lady Paramount birthright, The North, as the last and eldest Stark they know of.
They would be just hunting tapestries and not Baratheon hunting tapestries if they didn’t have Baratheons in them. Hunting needs people to hunt. Other-wise they are just nature scenes.
I assume they are Baratheon tapestries because they belonged to House Baratheon. Commissioning someone to make a tapestry is a huge financial undertaking. Who else would be in the tapestry but Baratheons if you agree there are people in them, and you need people to be in them to be hunting tapestry. Hunting involves people (their wolves, hawks etc) and the target prey. It would not be a hunting tapestry without the people. So a good assumption would be is that these tapestries have black haired blue eyed Baratheons hunting in them.
The tapestries haven’t been described in detail yet. GRRM is waiting on that reveal.
Littlefinger is a Loki figure, an agent of chaos. He needs the Royce’s to support him in his big upcoming move.
The Royce’s are the Vale’s (Ned) Starks; honorable beyond the point of it making sense. So Littlefinger needs the Royce’s to support him and for that to happen he needs the reason for them to support them to be the logical, honorable thing to do.
Cuckoldry of the king, is a pretty dishonorable thing, no?
Hat tip to the brilliant Nfriel, who if I am not mistaken said something very similar about the tapestry being a DNA test in a podcast.