Well, Soxy, I make no attempt to find reasons to think people ignorant. I look for reasons to think them bright and thoughtful.
Occasionally, I'll run across a person I consider ignorant. When I do, I shun them like the plague. More frequently, though, I find people much brighter than I, people with deeper insights and broader perspectives. From them, I learn.
As far as the two scenarios you described, what basis would I have to consider either one ignorant? Should I do so because they hold a view I don't share? That doesn't make sense. If I only respect people who share my views, what can I learn? By dismissing them as ignorant, I cut myself off from investigating other matters on which their knowledge and experience exceeds my own.
I see no benefit in categorizing them as ignorant. That seems like a lose-lose proposition to me.
Fred