Well, religion used to be science/knowledge in the past and those terms got separated when monotheistic non-gentile religions took over. Religion was seen as a national identity story in the process and later on it was just devoured by the new Churches.
Saying that religion was important in antiquity or in Roman Empire times is accurate, but confusing this with the religion that had too much power and importance in the Dark Ages and the Medieval era is inaccurate. Religion was pretty much the school system of the past and this started changing centuries later with guys like Plato and Aristotle who were caught up 200-300 years later. Pythagoras for example and his school was probably considered the greatest "university" of ancient times, yet a millennium later they started calling it a cult.
I'm guessing if this is Rome or another ancient game, you will have some benefits for choosing a patron god or whatever, but religion won't affect your relations with others probably. Though it could add something extra, with Poseidon vs Athena like the story of Athens
And they are not saying religion will not be important. It just won't be the most important.