You can be too open minded. It has gotten to the point where there are people out there are thinking pedophilia, rape, and murder is okay for "shock value" and that is bad. People keep saying "well if that's a countries culture then that is okay you have to be open minded". No. There has to be a limit. Don't give me that "morals are a matter of perspective". That is the same thing as saying you can just do whatever you want.
Closing your mind means that you no longer perceive. The mind can not function without input or data. By inference closing your mind means that some perceptions, observations, or memory is discounted rather than used in making judgments. This means that you will be wrong more often that the mind that is open.
The progress made by mankind in the recent centuries is a result of testing ideas scientifically rather than relying on historical thinking. To close your mind is to preclude further progress.