"Open-minded" is one term in a slew of identifying terms. As with any identifier, the term means many things, probably too many. An excess of meaning is tantamount to a paucity or complete lack of meaning. I am going to parse out what being open-minded means to me, balancing positive descriptions ("it is" statements) with negative ones ("it is not" statements).
When I identify as open-minded, I am doing so, because I perceive my beliefs and philosophies to be open to criticism and construction from within and without. The obvious metaphor here is a door. When an opinion dissents from mine, I keep the door of my mind open to that view.
Just because a visitor arrives, doesn't mean they will stay. Intellectual hospitality necessitates temporariness in some situations. To let any and all differences take residency would result in logical contradictions. Open-mindedness exists within the realm of logic and sense. I am open to listening to your views and I hope my interaction with your position to be mutually beneficial, but I may disagree with you in the beginning and in the end.
Some disagreements are simple matters of taste and opinion. Some disagreements are more significant, but without negative impact on anyone. Broadly speaking, theism and atheism are in this category. Before getting into the various permutations of theism and atheism, neither of these view points necessitate a negative impact on society or a lack of ability to collaborate for mutual growth of individuals, communities, and the environment at large.
Some beliefs hurt people. Anti-semitism is such a view. Racism is such a belief-system. Eurocentric, androcentric, and heterosexist positions are further examples of hurtful biases.
As with any other identifier, it isn't always true. Christians aren't always Christ-like. Libertarians enjoy some areas in which the government is involved. Heterosexuals have crushes on and enjoy physical contact with people of the same sex. People who identify themselves with a cultural definition of "masculine" have "feminine" sides.
Similarly, I am open-minded, but my mind is not open to somethings like anti-semitism, racism, eurocentrism, chauvinism, and heterosexism. I still can benefit from other views people in these groups hold, but I cannot imagine ever accepting their positions on equality. I think I listen to their beliefs, especially since I used to hold some of them. But from everything I've heard, they have nothing new to say. It is just the same old, misguided song and dance. I hear from them what they hear from me and neither of us do a great job at listening to each other.
Not only are they not saying anything new, but also they are hurting people. Just like open-mindedness does not mean being open to a slave trade based on race, sex, or economic status, neither does it mean being open to oppression.
In fact, it is precisely because of my open mind that I am against oppression. My open mind means I am for love, for love and reason brought me to an open mind. It would be outrageous and nonsensical to have an open-mind based on love and reason, but then be OK oppression and oppressive beliefs, to sit idly by while people are being actively hurt and discriminated. It is for this reason that I have dedicated my life (currently) to providing opportunities for college students to open up their minds: to do my part in fighting oppression and discrimination by influencing the development of college students.
I will continue to identify myself as open-minded, because I am. But I am certainly closed off to oppressive ideologies, because that is where the identifier falls apart, where it (self) deconstructs, because open-mindedness is built upon "closedness." (Get ready for my cheesy closing statement.) The open door defined by the closed, operating on the hinges of love and reason.