It depends on which conspiracy you’re talking about. What about the 9/11 conspiracy theory? I think the percentage of 9/11 CTers who are Democrats is much higher than it is for Republicans.
Why?
Because most 9/11 conspiracy theories say the U. S. government was involved, to establish American dominance over the world, or to provide an excuse to invade Iraq. Such a conspiracy would require the involvement of the Republican president of the United States, George W. Bush.