I am currently building a world where most of the realm is primordial and extremely hostile to human life with humans worship of an angel(With each angel being specific to that settlement.) warding off the darkness and keeping things solid. If the faith of the community falters then the protection bestowed upon them also falters which can result in a breach. How would such a society deal with someone who is found out to be a non-believer whether it be through their diary being revealed or them loudly complaining?
The obvious answer is exile. You don't believe? OK, pack your things and fend for yourself outside in the darkness.
The problem with your idea however is that any unbeliever who wishes to can simply mimic whatever cycle of prayer or ritual the community requires while personally having no commitment whatsoever to its ideals at all. And of course unless they are very careless no-one will ever know. Given the potentially severe punishment they face no unbeliever is going to talk about their agnosticism/atheism let alone leave written evidence of it for others to find.
The only circumstances where such might be possible would be where there is an organized 'network' or secret society of unbelievers who are hiding within one or more of the communities. That however would require some kind of backstory on your part to explain why it exists in a world where apparently faith is essential for mankind to survive. Perhaps for example they secretly worship the darkness because they believe (rightly or wrongly) that generations ago a pact was made by their ancestors with the darkness on the promise that if they could undermine the faith of the communities to the point where the towns collapsed they and their descendants would be spared/rewarded.
Just look at theocratic regimes on earth over the centuries.
Most will shun unbelievers at the very least, many will actively persecute them and either exile them, forcibly convert them, or kill them (often the same religion will do all three at different times and places).
And the true believers are excellent religious police, just make it a holy duty to weed out the heretics and either kill them or turn them over to the inquisition. You might even create a system where a new convert has to prove his faith by killing say 10 heretics for you, or by serving in a function in the armed forces where there is a very high risk of death for those who aren't true believers (I assume your deity grants special protection to his faithful on patrols in the wilderness and will withhold that protection from the unbelievers).
Frame challenge: there are no non-believers
In such a setting you can probably very directly prove the existence of angels. And very directly prove the existence of needing their protection. Assuming a non-believer exists, they can be convinced of real actual presence of all the supernatural things.
Such a society would most likely reinforce this by having demonstration of the reality of all of this.
Example of this:
Each year young adults (e.g., around 12-14 year-olds) might be sent to live out for a few days outside where there is no protection. This would be as much as a religious ritual as an actual practical example of an angel and their power existing. Adults can also be sent out to watch over the children and rotated each time. This both reinforces their belief and also they can serve a guides. When they leave the city, they need to make their way to the local shrine. Once there, they provide a prayer to the angel. This immediately stops the darkness seeking to creep into the shrine demonstrating this power. They live there for a couple of days maintaining the rites for honouring the angel. Once they leave, the darkness is back in full force. It is a dangerous journey but does show everybody involved that everything is real.
A non-believer later in life might be enrolled in the group. That should be enough to convince them that they are being foolish. Or they can even be made to make the journey by themselves and come back. A faithless one will surely perish. If they do have faith, they would return and be a fully functioning member of society. Win-win.
If there are a lot of non-believers, then perhaps the journey outside can be made traditional, so you go more often. And even if you do not, most other people would be thoroughly convinced of the reality of the religion. It would be hard to deny it when not only other people believe, they also can present concrete proof. And you can go see the proof yourself.