It can go both ways. I think a lot of that falls on the person approaching a person about a belief. I consider myself to be, for the most part, open minded. I have no problem with my beliefs being questioned or even challenged. Actually, I welcome that because I may have a perception of something that isn't correct and not realize it until something is brought to my attention. However, if someone approaches me and declares my belief as wrong or stupid, my mind closes immediately. Beliefs are personal and should be treated with respect, even if they don't agree with someone else's. This is so evident in the Hubpage questions. Read some of the responses to religious or political questions and you'll completely understand what I mean.
Yes, many people are extremely closed minded about certain things. But some are so opened minded, it makes you wonder if they ever had a belief in the first place. Even an open minded person will defend a belief until something or someone gives them a reason to change.
I find it easy to separate the two. One is willing to listen; one is not.