I like to look at my mind not as open or closed, but more as a nice screen door: It's "open" but things are definitely not allowed in.
I guess this is healthy. You can listen to a viewpoint that differs from your own - and maybe even directly opposes your own - and better understand how and/or why the other person/people think as they do. You don't have to agree with them and say "Well, I see what you mean, and I guess your opinion is as good as mine," you can instead say "Well, I understand why you think as you do now, but I still don't subscribe to your thoughts." Having a closed mind prevents this, as the attitude is "I believe what I believe and I know whatever you say is a load of crock and I don't wanna hear it," which allows for no understanding at all, and ultimately, no way to bring others to our own understanding is possible since we have essentially shut them off.