“Apophenia: the tendency to perceive a connection or meaningful pattern between unrelated or random things (such as objects or ideas).”
I agree with everything you wrote but I am unsure about this word and/or the suggested definition. The ability to see connections is a good thing; I guess the issue that seems to me to be harder is how to decide whether the connections are "really" there or not.
Other than for that definition, the rest of what you've said there seems probably something more like normal "gullibility" or "willingness to believe on faith without evidence" or "naivete" or similar words.