I think what you are describing is "tolerance," which is defined online as "able to tolerate the beliefs, actions, opinions, etc, of others." And I disagree with your friend, I do not think one can be too tolerant. Tolerance comes from an open and accepting heart. The world would be a better place if more people were like you. A guy at my work is transitioning to the opposite sex, and although I support his choice in a general sense, there is honestly something a little uncomfortable about it for me, I am ashamed to say. But I accept his choice 100%... it's his life, not mine, and I would never want to see him hurt or discriminated for it. Voltaire said, "I disapprove of what you say, but I will defend to the death your right to say it." That is tolerance.
Open-mindedness is defined online as "having a mind receptive to new ideas, arguments, etc; unprejudiced." Like if someone told you they practiced a religion that believed that God was inside trees, and so they worshiped trees, open-minded is saying, "Hey, maybe God really is inside trees, I will try worshiping a tree for a few weeks and see how it feels. I will put aside all the dogma that my parents taught me and everything I learned in church and see for myself." Tolerant is saying, "No, I don't think God is inside trees, but you go ahead and do your thing, I think it's totally great."
That being said, I do believe it's possible to be too open-minded, in a couple of senses. First, in a practical sense, it would become hard to really stick to things or make constructive choices if you were always open to every idea that came around. Someone would say, "Hey that's blue, not red," and your open-mindedness would force you to say, "hmmm... maybe it *is* blue."
I used to say about myself that I could be convinced of anything for 15 minutes. I was too open-minded. I was very confused by the "deciders" who knew what they wanted to do for a living, who they wanted to vote for, where they wanted to go to college, etc. So I just drifted, explored. It was fun, but kind of meaningless, because part of having a fulfilling life is taking a stand on things, believing in something, because if you believe in something you can work for positive growth (on the other hand, once you believe in *anything*, you sort of become part of the conflict in the world, but this can't be avoided anyway - you see? there is my sneaky "open-mindedness" creeping up, LOL).
The second reason I think you can be too open-minded is what I call "the close-mindedness of open-mindedness." Open-mindedness is rooted in rejection of absolutes. After a while you really reject ON PRINCIPLE any idea that claims to be THE answer. Like if someone comes to you, and says, "hey, this is THE WAY IT IS. Jesus is THE TRUTH." (i'm not saying he is or he isn't) You cannot even hear that, because you say, "wow, if I accept that, then I need to reject all these other possible answers, and that is unacceptable to me." After you spend enough time being super-duper "open-minded," you attach yourself so strongly to your "open" identity that you can't hear people of extreme conviction... you start think that they are wackos for believing so strongly in something that could be false.