With a lot of these things, it you need to talk to the players and discuss their expectations versus what (general) arc you have planned. You mentioned BESM, and if you're making the rioters fairly mundane people, the players can probably shut down whole riots as a single party without really much trouble unless some high level NPCs get involved. The system I have done the most class warfare with is 7th Sea (the players were a little too progressive for it to work in Victoriana, much to my surprise). By telling the players they are getting into a revolution, the group tended to come together on one side of the issues and their level of privilege. Some games involved the players living with commoners and brawling in the streets against riot busters and subversive goons. Other games, they had access to the nobility and never once saw a fight other than a personal, codified duel. Now, I'm not above throwing random chaos at the players but that's usually because somebody has a relevant skill that's been neglecting.
TL;DR - You need to have a talk with the players and their expectations/desires for the game.