I’d suggest that you start by reading David McRaney’s How Minds Change: The Surprising Science of Belief, Opinion, and Persuasion. You should also look into street epistemology, and Peter Boghossian’s A Manual for Creating Atheists.

First, I think that approaching this with the idea that you’re going to “change them” is probably not the correct approach. Rather, you need to approach it as a conversation where you’re hoping that you can better come to understand each other. Beginning with the idea that you will change them has the a priori assumption that you are morally correct, and that’s not necessarily the case. Is it better to do it in person? Absolutely. You will have a very hard time reaching real understanding online. You’ll need to do is find common ground, ask questions, and really, really listen to them. You need to be able to empathize with them. It’s also worthwhile to ask if they’re open to changing their beliefs, if they find conflicting information. (And ask yourself - are you open to changing your beliefs if facts conflict with what you believe?)

What you need to get at is underlying beliefs and fears, not surface-level stuff. You need to understand that these aren’t issues that can be solved with more factual information, because people will weigh facts through an emotional lens, and will weight things differently than you would to arrive at different conclusions.

On a slight tangent, when you talk about cult de-programming–which is controversial–the important thing to do is to utterly separate a cult victim from their support group, aka their cult, and then give them only one point of view. When you talk about deprogramming conservatives, you’re asking people to commit social suicide; it’s likely that all their close friends and associates (or all of their parasocial relationships) are with people that hold similar conservative beliefs. Without surrounding them with people that are more liberal, and are willing to accept them, you’re not going to be able to have a long-lasting effect.