Too Open Minded?

So there is this thing going around where people should be open minded. Honestly, its getting annoying. These open minded people argue that we are going into a new age and that we should shed the silly ideals of the past and go into the future with acceptance of everyone and everything. Okay, maybe thats not the whole argument, but the gist is that they want acceptance of everything. I can relate with the idea of acceptance, but some of these people take the idea way to far, and that is where it bugs me.
Let me say this, just to give some idea of where I am coming from. My dad is very conservative, and he doesn't like, well, I don't know what to call it, but lets just call it change. He is very firm in his beliefs of politics, and he never gives any credit whatsoever to the opposing side of a debate. Actually, he never really has debates, he just yells over the person he is talking to. He gets very adamant when talking about politics, but whenever I pose, what I would consider, a good question, he shoots it down as a dumb idea. He can't see both sides of a debate, he only sees his. What I am trying to say is this, when it comes to a debate, I really do try to understand what both sides are saying, which means accepting both side's viewpoints as valid.
So  yes, in a way, I am more "open-minded" than my father. I realize that a certain degree of open mindedness is good for the brain. However, many people can take this way to far. They start to accept things that are just wrong, or stupid. This goes past the political realm of things, and into every day life. Being open minded to things that can be harmful. Unfortunately I can't think of any specifics at this moment, so.... I'll come up with some later.