IM cannot be stopped. When a government broadcasts they will censor them, the very next step is for protesters to install something like Bitchat, which does Bluetooth-based, mesh/P2P IM-ing, and is specifically designed to resist even full-on Internet shutdowns.

The best way for governments to deal with protests is to have policies in place that fulfill what We The People want. Everything else is a band-aid atop an ulcer: it hides the problem for a little while, but the problem itself keeps growing regardless.