Anti-war demonstrations are a form of militant lobbying. Even radical direct action and civil disobedience aim to convince power-holders to do something different. This faith in government is misplaced.
The battle to remake society has begun. To remake it for the common good, workers must transform their unions into ones that fight for the common good. That means refusing to collaborate with capitalists and their police and orienting instead to the larger working class.
Socialism is the Best Medicine