The study basically says the more you are an intuitive thinker, the more likely you are to be a believer and to grow in that belief over your life. The more you are a reflective thinker, the less likely you are to believe. This leads some sidways support to the assertions made by the Oxford study discussed in this Atheist News Discussion Belief in God is part of human nature - Oxford study. (I took a lesson from Dallas Gaytheist's comment in that discussion and checked out the authors of the study and they seem to be very well qualified psychology and neuroscience researchers.)
In as much as "that religion is a common fact of human nature across different societies" a mix of intuitive and reflective thinking is also a fact of human nature. Of course the age of enlightenment and development of the scientific method specifically addresses this problem by recognizing that human intuition is often very wrong and seeks to eliminate it from scientific investigations by using objective methods and critical thinking.
This also highlights what it is about science that makes it so reviled by religion.