Between cult and your choice of terms... I think cult applies more. To me, religion is in some ways, a cult. On the other hand, a sect/parish/etc imply to me, a subset of a cult. The school isn't supposed to be a subset, but a superset. Which means "cult" still doesn't quite apply unless you take it as a typo in the manga... not "cult," but "cults."
It's like instead of a school for Catholics (a part of Christianity), it's a school that chucks Christians with pagans, shamans and Apple fanboys. *ahem*
@Reikou You don't need to be friends with everyone, but having less than a bare minimum of courtesy toward each other isn't great for people who're essentially working together. Schmidt hasn't been more than a sort of obnoxious classmate since the little contest thing, but they're about to go to a battlefield. It was better to find some sort of resolution if possible sooner than later so it doesn't become a thing at an inopportune moment when they were just taking classes together, this could quickly turn something life or death messier than it needed to be.
Sure, if its a job then you gotta leave all hostilities outside, but in a school setting? Against someone who already told you not to bother him? It's better to just avoid eachothers paths imo, specially if the other party is a dick.
And the only reason they're going to a battlefield together is because the MC is being pushy, which I believe has an equal ( Or higher ) chance of backfiring and creating even more trouble.
@Reikou Consider from the other end as well then, Schmidt needs to be mature enough to deal with pushy people he doesn't like in a workplace setting with high stakes.