Closed-mindedly

There's a balance between touting the equal merit of everything and being closed-mindedly opinionated, that I'm still trying to find.

Dogmatic people are often closed-minded, and dogmatically held beliefs are often closed-mindedly maintained; but a belief held closed-mindedly need not be held dogmatically: it may be maintained with a guilty realization that emotionally one simply cannot stand to listen to challenges of it, and with an awareness that it might be mistaken.