I have a two part test to figure out whether someone's a skeptic or a denier:
1. Ask them some sort of question about their position - "Why do you think X", or "How do you explain this weakpoint in your argument?" Basically try and put them on the spot a bit.
2. If they're evasive, then ask them what sort of evidence it would take for them to change their mind.
If they can't give a good response to either of these questions, then they're a denier - if you can't defend your position, and you're not going to admit to any possibility of error, there's not much point in arguing.
Those who are convinced should indeed start taking action.
>And where do you draw the line?
That's up to the person. Some people have a threshold so high it will always be beyond our grasp to meet, some have a threshold of "higher probability score than any alternative" no matter how low the probability actually is (e.g. 5% chance vs 2%, 1%, etc.).
>at what point do you stop arguing and take it as fact?
Again, it's up to the person. But again, if the person doesn't accept something as fact I'm fine with that. I'm not fine with them presenting their unconvinced-ness as some kind of alternative "theory".
>When are you allowed to start actively advocating a particular theory?
When you have one. "The other guy is probably wrong" isn't a theory.