FWIW, this is the same approach I take with members of Christian sects which have conspiracy theories within their teachings. Ie. The Jehovah’s Witnesses. JWs among other things believe that Mainstream English bible translations contain intention mistranslations used to justify ‘pagan’ doctrines like the trinity and the incarnation. If you try to argue with them you either get a memorised chunk of ‘Reasoning from the Scriptures’ quoted back at you or you get taken on a wild Goose chase through Daniel, Revelation and Ezekiel, etc.
In recent years I’ve started asking them question after question in more Socratic way. That is ask a question and then ask questions about their answer; trying to think of questions that draw out the conclusions I’d like them to come to. When asked in a gentle, genuine, and friendly manner, a questioning is a powerful, but indirect way to challenge to a person’s thinking. I’ve found that a good question can haunt a persons thinking much longer than a direct rebuttal.
You’re essentially teaching them to fish (arrive at the truth for themselves) rather than giving them a fish which they might assume is actually poisoned (a direct response).
Another benefit is that by asking questions you begin to understand the ideas as they understand it. This not only gives you a better insight into the topic but also them as a person (eg. Why the find it convincing, compelling, etc.). In turn this helps you craft better questions.
I would say that it does take huge amounts of self control to respond with a question and not a direct reply. It also takes a llllooooonnnnngggg time to see progress, but then I sometimes think more direct discussions only give the illusion of progres. Eg. moving through several topics whilst neither party move very far from their starting positions. However, if one love the person one invests the time gladly.
I hope that helps some. For anyone wanting some further reading, I’ve found the first half of Gregg Koukl’s book Tactics very helpful - the second half less so. I’m sure many of the principles of part 1 could be transferred to a ‘conspiracy theory’ context.