I hope someone mods some neat-o stuff into Fallout 4 when it comes out, maybe like Templar stuff. (I'm in a Templar/Medieval-Modern phase right now.)
Like this:

It even makes sense, since the war was basically the big ol' 'RESET' button.
Well Followers of the Apoc were pretty anti violence. They were only concerned with helping people by showing them the ways of medicine and agriculture, stuff you can build civilization and society around. The brotherhood of steel sort of fits into that knight thing.
Although if you wanted such a group you could do some world building and this is how I would make them fit in: Say there was vault, religious community that managed to survive in their vault. However this vault was only meant to stay closed for 50 years. The people of the vault used their geck to establish a settlement outside the vault. They got a pretty defensible position from raiders and wild life and there is also a town or part of the city near by their. Theres a church, some houses, rubble, and part of a library. Anyway the first few years were not good for this settlement.
They had been attacked by raiders, lot of people died from sickness, they did some trading, but they didn't have a whole lot to give away. There were some settlements in the area, but they were worse off than they were. They quickly learned the world was not a nice place. Anyway one day, one of the vault dwellers was scavenging the library looking for books on medicine, technology, and agriculture, however this guy is somewhat clumsy caused a few books to fall out of a shelf. One of them being a history book which flipped a section about the crusades and knights like the knights Templar. He read a some the book with interest. This guy was pretty charismatic as well and would eventually become leader of the group. Believing that the book falling was a an act of god he took the book as inspiration.
They soon take over the empty town and some of the surrounding areas and incorporating other survivor settlements. They'd use the resources available to them to start trading with other caravans and other settlements. Being one of the first people out the vault they had access to some weapons scavenged from the town as well as a local police station in addition to the weapons from their vault. They even had a small military force to defend their territories. They built their economy around farming, scavenging, and the trade of various goods either made or scavenged by them. They also have source of water under their control which makes the exportation of water profitable, although this makes them unpopular among various caravan and merchant guilds, primarily the water merchants.
However they learned from their early days that the wasteland wasn't a nice place. So they built a military starting with the surviving members of the vault security force. The church, library, and vault are pretty important places to them. They modeled themselves after the knights in the book. The most basic of them were volunteers and conscripts taken from other settlements, they were often called squires since they were the new recruits. Squires sport football pads and they might be given some sort of single shot homemade pipe rifle, or a homemade machete, or even a spear. The regulars are called Knights and sport metal armor and tunic similar to the Templar, they usually carry something with more heft like an smg, sledge hammer maybe, hunting rifle. Those that live long enough earn the title Paladin which sport a white advanced combat armor with tunic. Paladins will carry assault rifles, super sledge hammers, maybe an energy weapon if they are lucky enough, maybe have something like the bumper sword.
As you would have guessed they are pretty big on religion. They'll often send a missionaries to do missions and try to convert settlements with some knights to protect them. Some settlements or cities in the will have sort of base of operations in the form a makeshift church to try and convert people. Followers often make pilgrimages to the main church which they consider to be the most important holy relic of the old world.
The group is not without flaw. They are pretty charitable, they provide food medicine, and protection to those in need. However they only help those who will convert to their religion. They see themselves as survivors left behind by god to bring his word back to world inhabited by godless savages. So they made it their mission to rebuild society with secularism in mind either through force or by indoctrination. They are generally open to outsiders at first, but they'll become xenophobic to people who wont willingly convert to their religion. Sometimes they will attack settlements and try to force them into joining them. Other times they will "crusade" and wage costly conflicts against raiders and tribes as well as followers of different religions. Those that live in the under their rule sometimes aren't happy. Either because they decided that the religion isn't for them, or because of how the faction works. The faction is pretty conservative, often imposing gender traditional gender roles while women are allowed to join the military, but the a barred from leadership positions and are not allowed to rank up to paladin status; however they can find leadership position as a nun. Other criticisms include that they will often destroy valuable books of information which they have deemed evil. Such books might be science books or books on theory and religion. The faction often wages a lot of conflicts and has made their own regime unpopular at home due to the numbers of causalities that they receive from many of the pointless conflicts they wage. Some groups will unwillingly join them because its a better option than getting attacked by raiders and seeing their loved ones enslaved. The faction also hates robots due to their haywire nature and is often paranoid and cautious toward science. However they are somewhat open to science as long as it benefits them.
They are a medium sized faction with a decently sized territory. Most settlements are neutral towards them, while those who were annexed by force from crusades are often unhappy. They often hostile towards other cults and groups like the Order of the Proletariat.
I basically made them Midwestern Brotherhood of Steel lite, minus the obsession for technology, and their Bethesda brand Mary sue status.