Why do you think Stevenson shows his characters’ religious side only near the end of their adventure?

It's difficult to say, but it's clear that Stevenson does not want the story to appear as some sort of allegory or apologia for a given religious worldview. Nevertheless, precisely insofar as the characters' religious convictions shape their lives on a more timeless scale--giving them a lasting significance--it seems salutory to include them. This could be a reason for waiting until the end to mention them.