Religion is very important in every campaign I run.
I'm guessing your main problem with "religion" in your campaign is that you imagine religion in the way our culture deals with it in modern times. Here are a few suggestions that might help you to make this thing relevant in your campaign:
1. Remember: the gods and outsiders are real. There is no dispute about that. Everyone has to deal with them because they affect day to day life. Angering a god can cause bad weather, seismic activity, defeat in battle, etc. Obviously, it is very important for everyone in every sector of society that is subject to the whims of the gods/fate to either gain the favour of important gods or protect themselves from them.
Think of dealing with the forces the gods control in your world the way people in the modern world think about dealing with epidemic diseases or climate change.
2. Until the 18th century, many of the services we associate with government were carried-out by the church. They ran all the family law courts, dealing with marraige, divorce, property transfer, etc. They ran all the hospitals and almost all the schools too. As with things like crop failure, war and natural disasters, healthcare, education and the legal system affect everyone and are a matter of public interest.
3. The principle of divine right has, on and off, been an important one and not just a Christian one. Often, to be truly recognized as a king, one needs to be consecrated as such by religious officials.
4. Philosophies, political ideologies and religions have been hard to distinguish from one another for most of their histories. If people want society to work a particular way, or the government to run a particular way or for people to live a particular way in their day to day lives, it is often because one or more gods thinks this is a good idea.
If you're just getting the hang of how to make religion matter, start with these areas where the relevance of religion should be an obvious and self-evident truth. I might also recommend you look at some second edition Runequest materials which are excellent on this stuff, especially the Cults of Terror, Cults of Prax, Pavis and Big Rubble supplements. They give you a picture of an RPG society where religion is a big part of everyone's day to day life.
One last simple suggestion from a campaign I ran a few years ago: if you make your wizards' guild a tightly-controlled religious organization, religions should have a near-complete monopoly on magic in your society. That means that if you don't do what your cult wants, you can't really obtain rare material components, access to magic libraries or the right to purchase magic items.