Open Minded Irony

I was working with someone a few months ago and had an interesting discussion. He and I do not think alike and we do not have the same beliefs or opinions. He told me that we need to be open minded to other people's beliefs. I told him I am open minded. In my opinion, people can believe whatever the want. It doesn't matter if I think they're wrong, they still have a right to believe it. He didn't like that statement. He told me that by my belief someone's opinion is wrong is being closed minded.

That got me to thinking. Is he not experiencing the same close-mindedness by saying I am wrong to say someone else is wrong? My beliefs shape and define who I am. Many ideologies today leave no openness for oposing views. For instance, I believe action "A" is wrong. My friend Bubba, believes action "A" is the right thing to do. If Bubba ask me my views on action "A," and I do not tell him I think it is wrong, does that not belittle my convictions?