Specifically: is there something we can to to counter the feeling people get that they are being casually dismissed as irrational or stupid? Can we get them to see that "we are not so different, you and I"? And can you do it without them thinking you are playing some kind of mind game?
I know this is kind of an older post I'm addressing, but I thought I'd like to chime in on this based off my previous experience as a CTer. My info only applies to the experience I have, and I don't mean to tar all people who believe in CTs with the same brush.
Right now, I feel like I can trust that Mick or anyone else posting here is not a government agent. I can't bring up proof that MB is or isn't a government-run site, but my worldview is not one that allows that to be a plausible viewpoint. It is much much more likely to me that Mick was a former game designer, whose interests shifted toward the conspiracy realm because he found the theories fascinating and he enjoys discussions of science. Perfectly plausible and nothing unreasonable sounding at all to me. Lots of people are able to have huge amounts of knowledge about things outside their profession. I don't find that suspicious.
Yet, in the worldview of those more entrenched in CTs, there are government agents everywhere, the government works hard to suppress things they believe to be truths, and in their heart, they feel what they believe is already true...for whatever reason, so anyone going against that must be part of the bad guys. When one spends time in the CT world, it's easy to get your personal desires and identity wrapped up in the outcomes of fighting off the shadow government, that it is difficult to let that go and see that people can disagree with you and have interests in debunking conspiracy theories without being paid by the government. Anyone with an interest in debunking can only be someone who is trying to hide the truth, otherwise why would anyone be interested in this stuff?
I guess my main point is that if you are more paranoid, it is going to be difficult to trust anyone, especially on the internet where no one can pick up on nonverbal communication. I dismissed opposing viewpoints for various reasons because I didn't want to listen, and I don't think anyone would have changed my mind by continuing to poke and prod at me. I remember dismissing perfectly unaggressive people and arguments as being overly aggressive just because I wanted a reason not to believe them. I'd make up any reason not to.
I believed what I did and wanted to give myself a chance to see if it was right. When I got tired of it or saw my worldview was leading me nowhere, I was more ready to listen to opposing viewpoints.
Imo, the more you try not to make it a mind game, the more you sorta turn it into one. Being genuine can usually allow a less is more approach, where you don't try too hard to gain trust, which can be viewed as being deceptive.
Honestly, polite debunking and personally trying to see the human side of the CTer in a debate, is probably the best you can do. Those on the fence respond positively, and those further entrenched may have a seed planted in them where one day, they'll maybe see that their worldview isn't helping them or that it isn't leading anywhere.
I just think keeping an effort on being polite is the best thing to do. There are lots of aspects of interacting with people that you just can't control, and conversations with CTers are no exception. If they're willing to listen, they will. If they don't want to, do what you can politely, and then leave it at that. Keep it simple, imo. Trying to make the process more and more efficient (even through trying to appear less threatening than you already are in debate) sorta turns it into a game of trying to persuade the other person, but in a more subtle way.
I think the most that can be done is being done, except for maybe making sure that CTers that post here don't get dogpiled on by everyone. But other than that, I think what is being done here is as effective as it can be.