Was the Pink Letter the catalyst for murdering JS, or were the moutiners going to kill him anyway?
The Pink Letter was the excuse, but there is no such thing as a spontaneous mutiny/assassination - first you have to identify and organize those of your peers who agree with you, second, you have to create a plan for how you’re going to kill your commander and not be executed afterwards, and do all of the setup; third, you have to execute that plan.
And this is where I depart from a good number of ASOIAF fans who basically argue that Jon’s assassination was justified b/c of his reaction to the Pink Letter, because all of that work I discussed above had to have happened before the Pink Letter. Which means that the conspirators had already decided Jon had to die before he broke his vows openly, which is convenient for them, but in no way gets them off the hook for when they were making the call.
Which brings me to something I feel gets left out of a lot of Pink Letter theorization - predicting the fallout from that letter is pretty damn impossible. The letter gets sent to Jon and arrives “sealed with a smear of hard pink wax.” Unless someone cracked and then remade the seal, and that’s unlikely (Clydas isn’t the kind of guy to do that, and he’s not one of the conspirators), no one other than Jon at the Wall knows its contents. And no one can predict what Jon’s reaction is going to be - hell, even Jon doesn’t know what he’s going to do before he does it.
So all of the theories that rely on Jon bringing men south to Winterfell as the purpose for the Pink Letter are bunk. Ramsay wrote the letter operating on (mostly) bad information. Period.