I think it's a mistake to assume that conspiracy theorists or people making other outlandish claims fall into neat 'left' or 'right' wing boxes- I worked with a woman who believed most conspiracy theories, her views were all over the place politically and at best I would describe her as 'anti-establishment'. For e.g. one of her opinions was that Iran and Donald Trump were actually co-operating as part of the war with the deep state.
Her basic starting position was always that the state was lying to us, the reasons for that were often whatever fitted most neatly in her head.
I don't work with her now, but I could easily see that she would believe anything that suggested a fit-up or that the police had the wrong man.