I think 90% of those on the Far Left and on the Far Right believe the JFK assassination was committed by the evil, evil, evil CIA (or rogue agents thereof).
But the Left believes it because they think JFK was some sort of threat to the "national security state". He was going to, in their view, end the Cold War (or greatly reduce it), get out of Vietnam, normalize relations with Castro and so on. That is, essentially overturn the containment policies the US created after WWII. Plus, they think those policies were immoral and wrong and that the US was the chief cause of the Cold War anyway.
So the CIA had to kill him.
I don't think the Far Right sees JFK as that sort of president. They certainly don't think the Cold War was caused by the US, that the communists weren't a threat. So why they think JFK was killed by the "deep state" is a mystery to me.