I've got a few ideas that might help with this.
1) Be subtle.
Whatever way you end up going with this, don't make a huge deal out of it unless it's critical to the plot. If this is meant to be a piece of the background, then don't call attention to it all the time. I'd suggest that unless fire magic is related to the adventure or story arc at hand, only mention the prohibition against fire magic every few sessions, if that.
2) Make related objects hard to find.
Maybe this proscription against fire magic means that tindertwigs and smokesticks aren't available for general use. Maybe the only way to make lamp oil in this world is through the use of a fire magic ritual, so normal folks can't use lamps or lanterns. Think of some fire-related objects that are useful, but not totally necessary that make players notice their lack without penalizing them overmuch.
3) Make items that require fire more expensive
This is related to my comment above. Maybe swords are more expensive, because only the church and their personal blacksmith can cast the spell that lets you forge steel. Unless making fire explicitly requires a ritual, there are probably some "atheist" craftsmen that create things without using the rituals, but do so slower.
4) Give benefits to faithful players
If a player is a member of the church and sucks up to the high priests enough, maybe they get a discount on weapons, or access to some minor fire-related item that most people don't get.
5) Have the fire church wield significant temporal power
Fire is extremely useful, especially in the pseudo-medieval world that D&D is based on. The average person has a hearth, and makes a cooking fire all or most nights. The only real way to stave off the cold during the winter (or year-round, in colder climes) is through fire. If the only practical source of fire is the fire church, then that church will be very politically powerful, and might even be the primary political force in the land.
I'd also like to rephrase the question that I asked above: Is there any practical way for non-church-affiliates to create fire without rituals? Can a normal person light a fire in their home without fear? If people can't use mundane fire, then that is a super big deal, and emphasizes point #5 even more. In temperate areas (like most of Europe, for example), it's nearly impossible to survive a bad winter without some kind of heating for your home.