There is a significant difference between critical thinking and the psychological factors involved in those who embrace conspiracy theories.
When we embrace theories like the moon landing being false or that 9/11 was an inside job, we are displaying high levels of distrust and low agreeableness of and for authority.
This can be a temporary response to leaving a religion or cult behind, especially when the subject does so due to suffering abuse. It is generally part of the healing process, often typically normal, and will likely diffuse itself with time. Rarely do people get stuck in these periods of distrust, and if they do it is usually a sign of a more significant problem, such as mental illness. Until this the subject will not reconcile certain facts of reality until they can feel safe, remaining antagonistic up to the time healing occurs.
It is best not to argue with someone in this stage of transition because part of what is happening is important to their emotional growth. They are learning that they can reject significant things in life without the punishment promised by religious authority.
The conspiracy also helps them deal with displaced projected anger that has nowhere else to go. And the reason such people cannot be reasoned with is usually that they cannot process further in-depth information at the time. A healthy form of compartmentalization sometimes shuts off our higher reasoning functions in order to place us in "survival mode." Until we can can learn to be safe without repercussions for our convictions (something cults and certain religions tell us we cannot be), we have to take tiny mental steps, confirming for ourselves that we won't be punished for independent thinking.
But it can be scientifically demonstrated that the landing was real, and nations still send probes there and take pictures regularly sending them back to earth up to this day. And as mentioned before, you can do things like bounce light off reflectors placed there during the landings and even see the actual landing sites with proper instruments.