Oh I can help here, I'm an expert on this one, my wife can attest to that!!
My rigid thinking comes in the form of me always thinking that I'm right and there's no other possibility. I've come to realize that oftentimes you can be right or you can be kind, but you can't be both, so I've learned to "let it go". Even when I let it go, usually I still believe/know that I'm right and I'm just letting others have their way because I don't want to be called a jerk anymore.
I will say, I've always welcomed other people's arguments. My positions are well-reasoned and based on logic. If someone presents me with new facts or rationale, then I'm open to changing my mind. Actually, I don't view it as my choice... Logic leads me to an answer, I don't choose an answer, hence its rigid. But anyway, I can count on one hand how many times that's happened. Most people base their conclusions on emotions, and I'm not interested in hearing that.