In the many conversations I’ve had with my friends on conspiracy theories, we usually end up talking very loudly at each other. It may even sound to someone watching us that we’re yelling at each other; I know it feels that way to us. Often we’ll call attention to this fact and talk in quiet tones, only to start back up again a bit later. I call this “,” and it seems we can’t do much about it.
This is too bad, because the last thing you want to do in an argument is make something personal. It’s the quickest way to offend the person you’re arguing with, and that person might be a friend or family. Our ideas make up part of our worldview, and when you attempt to tell a person why you think they’re wrong, you’re basically saying to them, “You know, I think you’re an idiot for believing this,” so these discussions already start out heated.
One thing you can do is address the arguments, and not the person. The argument is bad, not them. Remember that the person is not crazy for believing something, they’ve just been misinformed– if they have indeed been misinformed. Tell the person that you don’t think they’re stupid or crazy outright if you have to. Try to sympathize with how they came to believe what they did, even if you think they’re wrong. In debates about conspiracy theories, I’ve had to do this a lot.
Try not to include them in any talk about hypotheticals, and don’t use the word "you" when you can avoid it (by this logic instead of by your logic, if someone did x instead of if you did x). This avoids putting them on the spot, which usually triggers an emotional response, only adding to the tension.
Also, if they are relating personal testimony (prime opportunity for offence) to you and you don’t believe it, be sure to state that it’s simply that you don’t believe personal testimony without evidence, or emphasize the commonality of being mistaken (again to ward off accusations that you think they’re crazy).
Nothing good comes from offending anyone. If it’s someone you know, it can strain your relationship, and if it’s someone you don’t, you’ve at least failed to convince someone, and you’ve made yourself look like an asshole in both cases.