I suggest "consistently inconsistent" might accurately be used when evaluating the behavior or a particular person across a range of issues. For example, if an individual's words and deeds are routinely inconsistent, misaligned, and inaccurate in context of a range of policy issues such as immigration, national security, and international trade, human rights, the rule of law, etc., said individual might accurately be described as consistently inconsistent.
Consistency of word and alignment between words and deeds being so closely tied to credibility, one might also describe said individual as "incredible" -- literally the opposite of credible, and arguably therefore untrustworthy. (Though of course affective trust is often granted despite numerous indicators that cognitive trust should not be.)
[NOTE: In light of the high likelihood one might infer I was referencing a specific national leader in this example, please take my example at face value. I'm confident it will stand on its own merit; if it applies accurately to any given individual, that's not my fault.]