The majority of us are probably not capable of building, in our head, a truly consistent and accurate model, or even a set of rules. Instead, we use abstractions and heuristics to help us associate different ideas. Using these heuristics, for example, we can decide whether some policy fits our worldview (e.g. whether a libertarian should support countercyclical monetary policy). But, these stories that we come up with to justify our decisions are necessarily based on limited information, so there is some probability that part of the story is wrong.
Is consistency important: sure. Should it be a standard by which to judge independent ideas: I don’t think so.