Numa Denis Fustel de Coulanges also claims that the broadening of the Greek and Romans' ideas of god from something domestic and family/city-specific to something that had dominion over all men, and the transition away from worship of the sacred fire, was propelled by a "strengthening of the mind."
This is true in the specific sense that he's using the term "religion."
The New Testament statement "The Kingdom of God is not of this world" is revolutionary. It disagrees with Judaism, Roman law, and even with Islam where Jesus is included as a prophet. Sincere belief in the Gospel's claim has caused political dissent for almost 2000 years. This is what Coulanges is referring to.
You have to be careful because the word "religion" doesn't have an objective definition, but Coulanges uses it in a consistent way.