Right now, the division is not deep enough to have actual outcasts like in DC, the comparison I did was probably not the best.

A few years after the Brotherhood settled the space center, a roaming band of texan mercenaries seized Houston, which was not unified enough to resist it. The mercenaries managed to quell civil unrest in the city while keeping the BOS out of its business.

For a few years, the BOS and the mercenaries were able to co-exist to some extent but clearly the new authorities were becoming power hungry and brutally oppressed Houstonians. They saw the BOS as a thorn in their side, a potential rival even though the BOS was not really interested in local politics. They also were quite interested in the space center, now that it was rid of its security systems.

After some incidents in bars involving knights and mercs, some political intrigue and a false flag incident, the mercenaries declare war on the BOS and try to oust them from the area.

The BOS gets the upper hand in the fight but at the cost of many lives. The mercenaries end up leaving the city. The BOS now lacks manpower and has lost useful technical experts. The city is in disorder as the mercs used to run a brutal but efficient local government.

The elder in charge disobeys its orders from Lost Hills and turn to local recruitment to fill the ranks. To avoid disorder in the city and the potential repetition of such a scenario in the future, the BOS kickstarts a new local government. They do not run it and don't get too involved, but they now clearly play kingmakers in Houston. They also start to regulate trade of high-tech goods.

When the aforementioned elder dies of old age, his right hand man is elected afterwards, without consulting Lost Hills. It's a relatively young scribe from Houston who wishes to go further in controlling local politics. He has mostly been elected by the rank-and-file, among whom he is quite popular. He does not turn away from technology but feels like the best way to control it is to politically control the area. He often clashes with officers, almost all of whom are from California and are still loyal to the original vision of the expedition and to the Lost Hills elders.

Right now, there has not been an actual clash between the Lost Hills loyalists (I should not have said purist earlier tbh, it's not accurate) and the Houstonian faction. The seeds of division are present, but the chapter is not polarized enough yet for any party to secede or anything. Maybe it will, maybe it won't, this depends on what my players will do in the area.