How to Remain Open-Minded

How do you maintain an open mindedness without sacrificing your core convictions? What i found most helpful is embracing a mantra that came from doing comedy classes with my husband and spending a lot of time analyzing what goes on in improved comedy theatres. One of the philosophy they live by is that curiosity and judgment can't coexist. Saywhy is it that a person as smart as he is thinks so differently about this issue? I get curious. I ask questions. I want to learn.