Bias IS normative. We all have it, mostly in ways that we aren't even conscious of. The biggest impediment I see to critical thinking and logic comes in the form of people being run by their emotional responses from behind the scenes to the point that they can't even recognize flaws in their thought processes. This annoys me but doesn't surprise me, since cognitive science confirms it.
"The unconscious places are influenced not by logic but by embodied primitives, frames, conceptual metaphor, and conceptual integration. All of our deepest ways of making sense of the world are unconscious and they are heavily influenced by what they have been exposed to, particularly in childhood, although current influences also come from things like the media and who we spend time with."
More than once I've written something very clearly and because the other person is having an emotional reaction to what I've said, they are missing whole segments of what is right there in black and white. I'm not talking about things that need interpretation. I'm talking about concretes that are right there on the page clearly stated, but because the other person is reacting and not responding from a place of cognition, they can't see what is right there. In a conversation about whether thinness in women is desirable as a cultural thing or an evolutionary thing, I mentioned a relevant scientific study.
The guy I was debating said, "The study you mention uses only BMI, not measurements, so it’s not directly useable for this argument." In fact, it clearly did not only use BMI. My response: "The study I cited used hip to waist ratio as well as BMI. I’ll refresh your memory with what it said - 'William Lassek and Steven Gaulin, anthropologists from UC Santa Barbara, have reviewed the research on body shape, attractiveness, and fertility. As well as waist-to-hip ratio, they looked at the impact of body mass index (or BMI).' He still didn't SEE it and I had to quote it one more time because it so went against his deeply held beliefs that he just sort of tuned it out. This happens ALL.OF.THE.TIME. when people are deeply emotionally attached to their point of view, rather than seeking to get the best sense of what is actually taking place (within human limits, of course).
None-the-less, practice over time of learning to examine one's thoughts and challenge them can help improve this. I often ask clients to evaluate something with a positive interpretation of the situation, a negative interpretation, and a neutral interpretation. This helps them to realize that the filter they are used to seeing something through isn't the only possible one. Facility with looking at several interpretations of something means that you are more likely to come to a conclusion that isn't simply rooted in subconscious drives. It doesn't absolve you of all implicit bias of course, but it does go a long way toward being able to think more critically about something that has an emotional charge to it.