Before turning his back on Hydra in The Umbrella Academy season 2, which was set against the backdrop of the Kennedy assassination.
It's easy to miss, but in the MCU there really was a conspiracy behind Kennedy's murder. In Captain America: The Winter Soldier, Steve Rogers looked at photos representing the Winter Soldier's past kills; one of the most prominent referred to the Captain America: Civil War, where Tony Stark would learn how his parents had died. But in the background there were also shots from the Kennedy assassination, clearly implying he was killed by the Winter Soldier under orders from Hydra. All of which raises the question: why would Hydra want JFK dead?
Historians have delighted in trying to figure out what would have happened if anybody had lived. It's anybody's guess whether or not he's have won the next election, but if so Kennedy's second presidency would have been a game-changer for the United Sates. There's some evidence Kennedy would have resisted pressure to escalate the conflict with Vietnam; in fact, the day before traveling to Dallas he had ordered an in-depth study of every feasible military option, including withdrawal. Meanwhile, Kennedy would have been interested in establishing a rapprochement with Cuba; he believed it was necessary to deescalate tensions with Cuba, distrusting the views of his military advisers. Back in the early '60s, Hydra was undoubtedly working to cause as much instability as possible, and this would have made JFK a true threat to their longer-term goals.
But the threat of John F Kennedy could well have been a lot more direct than that. In Captain America: Civil War, there is a photograph showing Peggy Carter with JFK. The early SHIELD was restricted to the United States, and they appear to have played a key role in the Cold War. The photograph of Kennedy appears to have been one of Carter's most treasured possessions, suggesting they worked together particularly closely. It's possible this partnership was close to uncovering Hydra's presence. Hydra was active in both Russia and the United States, and Kennedy had his own channels to the USSR, which could have hinted at a grand conspiracy.
Bucky Barners will return in the Winter Soldier conducting assassinations for the US Government in order to earn his continued freedom. If so, conversations could shine a light on some of the crimes being held over his head - including the JFK assassination.