Ryu left the old man's information shack moments later, not asking about the Battle of Faith. He had a keen understanding of which questions he could get an answer to, versus which ones he very much could not ask without raising suspicion.
The question of Battles of Faith was most definitely one of the latter. This was the reality, and he had to be cognizant of that.
But it wasn't as though this was the end of the world, after all, he still had the little woman, and not long after he left, he asked her the burning question.
In Sacrum, Faith was important as well, but it was more illusory. However, he remembered long ago that he had learned from Sarriel, that in the True Martial World, Faith took physical shape in the form of a well spring of sorts. In order to truly destroy a Sect or Clan, this well spring had to be destroyed first, and if this wasn't done thoroughly enough, there would always be a chance for a comeback.