It's a form of protest -- meaning a challenge or accusation levied against the powerful by the less powerful.
Such things are inherently dickish and often a bit petulant. Our evolutionary forebears liked to fling their own feces to express these kinds of emotions. We do it symbolically. Go listen to some punk rock.
https://www.youtube.com/watch?v=R8fLOJswWtk
https://www.youtube.com/watch?v=CAaQtDUNZHk
"Punk" style and sentiment isn't popular around here -- this is largely an upper class forum full of top-ten university graduates. When the system is good to you, it's hard to understand why others hate it so much that they're willing to engage in this kind of petulant rage-driven feces-flinging behavior.
Having been raised in a barn in the flyover country on food stamps, I personally really get it. I do not think Apollo was a hoax, but I do think advancing that crackpot theory is a good way to say fuck you to NASA for losing the will to actually go anywhere and to the US government for deciding that Vietnam was more important than humanity's future.
The "fuck you beliefs" effect is IMHO a bit broader than I implied. One of the reasons people are not vaccinating their children is that the president lied to us about Iraq. That's because if you are middle to lower class, the "authorities" start to look like an unreachable monolithic bloc from your perspective... like how a light source loses detail and vanishes into a point at infinity. This effect is magnified if you are both socially and physically distant from your authorities -- which is why a number of these beliefs are much more popular outside of coastal alpha world cities.
Edit:
I thought of another way to explain it, returning to the moon hoax theory...
If you are living in an underwater house in the flyover country somewhere and are working a dead-end job to service that and your mountain of student debt, "we" did not go to the moon. They went to the moon -- the same they who hold your writs of indenture and tell you what you must inject into your children. That "accomplishment" is one of the things they lord over you, so denying it is a way of denying their authority over you. Not vaccinating your kids is another. You don't have the power to escape your socioeconomic situation, but you do have the power to do those things. Protest, like water under pressure, will find whatever holes in a structure it can.
This process is only semi-conscious, and is driven by emotion. The process whereby an elite comes to believe itself above law and decency and to lord its "meritocratic" status over people is also only semi-conscious and driven by emotion. We all share 99.9~% the same genetic material, and none of us are perfectly rational beings.
The popularity of these "antagonistically irrational" beliefs is a major leading indicator of social trust collapse. This will be followed by the collapse of our society, since mutual trust is the basis of civilization. I think the rolling out of things like the surveillance state are due in part to our elite's understanding of this coupled with the fact that they lack the spine to take the high road and actually repair their lost trust by owning up to past mistakes and offering to remedy current wrongs. This in turn will only accelerate our social collapse as people, contrary to popular belief, are not utterly oblivious and see these moves for what they are.