should I go ahead and add random people that has not been trusted by anyone in the forum to my distrust list?
No. That would mean you can add a few million users, it's useless.
Or whenever we are discussing in a thread, anyone that doesn't agree with my opinion once or twice, I should add them to my distrust list?

No.
You can add me now, I disagree.For the record, there's nothing wrong with having a different opinion. Some people seem to think that's the end of the world nowadays, but really, it's fine.
You can even include someone who excludes you.