You are confusing unwavering with stubborn. A stubborn person would not react to new evidence that invalidates their beliefs. An unwavering person would.

The only information I have relates to the outcomes of their decision process: speechs they give, statements they make to media (or reported by media), bills they sponsor, their voting record, etc.

Because this is all political theater, I don't even really know what they are actually trying to do by making these statements, these votes, etc. So there are at least two layers of obfuscation between the ideas a person holds sacred and my ability to measure those things. The result, is that when we say a political figure is unwavering, we really just mean that these little plays they act out for us always have the same theme. Even if their beliefs change they cannot afford to rewrite their own character in the middle of the scene. That would just be confusing. Better to bring in a new character entirely.