Open-mindedness was the willingness to consider new ideas. Closed-mindedness was the unwillingness to consider new ideas.
In 2152, Trip Tucker caught members of the Takret species having a barbecue next to a plasma manifold aboard the Enterprise NX-01. While Tucker understood the crew were explorers who were supposed to keep an open mind about different cultures, this was one of several reasons Tucker cited for driving him crazy. (ENT: "The Catwalk")
In 2365, Captain Jean-Luc Picard told Wesley Crusher to open his mind to the past, including art, history, and philosophy. (TNG: "Samaritan Snare")
In 2368, Worf was left paralyzed after his spinal cord was crushed. As a patient in the USS Enterprise-D's sickbay, Worf was described by Doctor Beverly Crusher as being in full Klingon mode; honorable, strong, and closed-minded. Crusher welcomed Picard to check in on Worf, but told him not to expect a lot of conversation. (TNG: "Ethics")
In approximately 3074, Quarren re-activated The Doctor's EMH backup module to talk about what really happened seven hundred years before with the USS Voyager. In response to The Doctor asking if Quarren was willing to listen to a "mass murderer" like him, Quarren stated he was willing to keep an open mind which was the most he could promise. (VOY: "Living Witness")