A civil war because an 11 year old girl didn't lose fifty house points as well as the detention she got as punishment for being attacked by 44 students? When, mind you, Lucious's son had been backing Hermione himself? That's just absolutely absurd.

The wizarding community in Magical Britain is pretty close to civil war in general. The community is small so small scale results can have larger impact, and Hogwarts is the only magic school in Britain so people pay more attention. Moreover, the wizarding world has a lot of values based on medieval ideas. In Roman times people fought wars over chariot team winners. In modern times that's translated into wars about football.

The idea that discipline issues could be a significant enough dispute to push them over the brink is not implausible.