I am slow and lazy today, so please forgive if I am asking for the obvious:

Do the referenced studies control for the process of acquiring education/intelligence, and test for causality?

It seems that a plausible competing hypothesis for the correlation between intelligence and, for example, religious belief, are:

• the process of acquiring intelligence leads to removal of biases, rather than actual possession of intelligence leading to removal of biases. If we change to a different process for acquiring intelligence, we may lose side effects.
• the process of disposing of religious beliefs leads to a more measurable or noticeable level of intelligence.
• the process of becoming educated in current education systems (and as a result better exposing existing intelligence aptitude) works at eradicating certain sets of beliefs and biases in students

It seems to me that differentiating between data that supports these hypothesis is incredibly hard, and I wonder if the referenced researchers went to the lengths required.