It's best to be aware of both. Yes, you may meet trolls and hardcore believers of some really stupid things, but if you always assume that anyone who disagrees with you is one of such people, you're bound to end up as one of them yourself.

EDIT:

Perhaps this is another skill, related to counterfactual analysis: being able to consider you're wrong just a tiny bit, even if you're certain you're right, just to reaffirm yourself. Holding the two conflicting states in your mind, in parallel, for however brief a moment. Kind of like speculative execution. Doesn't cost much if the other party is an obvious troll, but can pay off handsomely if you somehow ended up with a strong belief based on badly flawed assumptions.