Introducing a Fantastic Religion to the Players

[Unoriginal]

If you want them to have an insider's perspective, you have to prepare a primer for it

In practice, this entails making a setting book or booklet for them to read

You can just tell them what their character would know about it when it is relevant.

No need to write anything.

"You know that today is the day where worshipers of the Celestial Carp would usually be gathering and celebrating their deity in a festival open to the public. That the shrine is empty means something very wrong or very weird is going on."

Or

"Then the Duke, visibly livid, turns to his brother and says "I swear by the Sun and the Moon that if my son isn't freed by nightfall, I will storm the prison. I don't care if you're the Minister of Justice now, you don't have that right!". Steve, since your Wizard follows same the religion as the Duke, she would know that swearing by the Sun and the Moon is the most serious oath one can make in such circumstances. If the Duke doesn't do what he promised, he would be treated like an honorless oathbreaker by every member of the Sun clergy or the Moon cult in the country, and that would essentially destroy his political support."