I think we must remember to mention "rationality" in such conversations whenever we speak of things like "rigidity".
Rigidity is a kind of irrational stubbornness, and unwillingness to consider alternatives when reason compels otherwise. Someone who is principled and has a reasoned basis for his principles isn't stubborn or rigid. He's principled. His certainty isn't irrational, because it is rooted in the best justifications he has, perhaps even very good justifications that have successfully resisted all counterarguments he has heard, perhaps justifications that necessarily follow and could not be otherwise. Certainty is not a sin if rationally justified. Indeed, there is a performative contradiction in claiming that it is with certainty.
Good point, those are totally different things, but it is often hard for someone else to tell the difference unless you explain.... explaining can also be a complex issue in office politics, because some people will see explaining as seeking and requiring their approval, and therefore subordinating yourself to them.