While all the answers provided so far probably have some influence on people’s willingness to believe CTs, I suspect that you are falling for the same type of fallacious thinking that many CTers fall for, namely, thinking that there IS an answer, that there MUST be an answer to the question you’re asking.
I think this applies to people’s beliefs, too. Some of us make some sort of conscious effort to make sure that our beliefs correlate with reality, but many do not, and very few do so thoroughly and rigorously. Even for the most rational of us, correspondence with reality is only one of a large number of variables influencing what we believe, many of them random and uncontrollable.
False beliefs like CTs are not the exception to the rule; they ARE the rule. Human minds are FULL of false beliefs, and we correct them only when there is a clear, immediate benefit (often a social benefit) to doing so.
Remember Click and Clack’s Car Talk? Think about how many people called up with false beliefs about how cars work. Think about how many false beliefs exist in any organization about the best way to do something, just because no one has ever questioned it (and questioning it might be costly and wasteful compared with doing it the way we know). Think about how many assumptions we make about the the people around us without ever trying (or even being able) to verify them.
CTs are just the most interesting ones (which probably helps them spread) that attract the attention of the rest of us. No one notices or cares if someone thinks they have to warm their car up when its 30 degrees out, or that the cashier was rude because of the political button you were wearing, but we all notice and comment when someone thinks the moon landing was faked or the earth is flat.
In truth, all of those beliefs were arrived at through the same drunkards walk of mostly random speculation and lack of verification or falsification. Most of us haven’t verified that the earth is round, but we live in an industrial society where there is some practical and economic value to having correct facts about the shape of the earth. Most of us (outside of rocket scientists, airplane pilots, logistics coordinators, etc) aren’t affected by that directly, but it’s enough to shift the social pressure in our culture such that there is enormous social value in agreeing that the earth is round. But some of us are far enough removed from the small segment of society that actually benefits directly from having correct beliefs about the shape of the earth that false beliefs can fester and even form their own pockets of society in which false beliefs have social benefit. Not for any particular reason, but just because for those people there is little benefit to being right.