Based on my experience here, there doesn't seem to be any particular link between political affiliation and belief in a JFK conspiracy. Some on the right might be prone to entertain anti-government conspiracy theories but they are also more accepting of facts and logic which point to Oswald. Some on left like Oliver Stone may not want to accept the conclusion that a Commie killed their leftist icon and entertain a conspiracy by default.
Gallup poll last year had these results. The Republican/Right in this survey is now more likely to believe in a conspiracy than the Democrat/Left: 71% vs. 55%. I think that's a recent change? And this is not just the extremes, the far left and right, two groups that I think are even more likely to believe in a conspiracy. Probably in the 80%+? 90?
The Right's increase probably comes from their "Trump collusion allegations were falsified" complaints - i.e., that the FBI and CIA went after him using lawfare tactics. What else could it be? Nothing new has come out to cause this increase. I don't think they've been reading Jefferson Morley's ramblings.
So the "deep staters" got JFK like they tried to get Trump. Boy, that's really silly. How does what the FBI/CIA today - a different generation of people - supposedly did to Trump tell us anything about the JFK assassination some 60 years ago. These are two entirely different generations of people. Comey is Hoover? And who is Dulles? Two different presidents. And two different times. One was lawfare, the other overt violence. Gosh, this is dumb. BTW, why didn't this supposed "deep state" use lawfare against JFK instead of shooting him using this Byzantine conspiracy?
Anyway, yeah I don't see any political linkage - left, right and center believe in a conspiracy - but it seems to me that the major proponents of a conspiracy over these years, the ones getting the most attention and keeping the idea alive, have been from people on the Left. How many college kids brains did Mark Lane screw up with his lies? Garrison called himself a libertarian/conservative but his view of the national security/Cold War state is right out of the anti-anti-communist Left. Viz., the US "war state" as he called it was the chief cause of the Cold War. The other major figures - Oliver Stone, Mark Lane, Sylvia Meagher, the Ramparts Magazine people, Vincent Salandria - were all leftists. So while there's no direct connection between party affiliation and conspiracy belief I do think the main forces pushing the idea have been from the Left.