What are the psychological and sociological factors that cause religious belief to be so strong that many people cling to it over rational thought?
Psychologically, when people have a problem it's hard to conquer it if they are entwined with the problem. If they are a part of the problem it's hard for them to accept that and find a solution. So, believing in religion is actually a form of externalization. What a problem is externalized, you could talk about it and conquer it much more easily. For example, fear is having an effect on me vs I'm so scared I can't do it. It's more empowering to externalize something and then take care of something.
It's my belief that some people don't have the self-control to get their shit together on their own. Some people need to believe that there's a higher power up there that expects them and wants them to do certain things. So, they do the right thing for the higher power rather than hold the responsibility themselves, and possibly not do the right thing because there is no one holding them accountable but themselves.