The basic problem for CT'ers is, there are a million different ways a Conspiracy might've occurred and there's no consensus on the CT side for an alternative narrative to contrast with the LoneNut narrative.
So LN'ers often delegitimize CT'ers by grouping people who have plausible alternative theories with those who believe JFK might've been shot by the "Umbrella Man" or the "Three Tramps".
The problem I see for LN'ers is the failure to acknowledge the legit reasons to question the interpretations of the evidence or the conclusions of the various investigations.
It's possible that in spite of mistakes, the coverups, the obstruction, the lies, etc, that the LoneNut narrative is the correct one. But you have to leave a lot of valid questions about the investigations unanswered to be satisfied with that narrative.