The phrase "peaceful demonstrators" refers to people who protest or express their opinions in a calm and non-violent way. They are taking a peaceful approach to convey their message or advocate for a cause. Full definition
The hoses have iconic significance in relation to the civil rights struggles, in particular with regard to the hosing of peaceful demonstrators in Birmingham, Alabama in 1963. (artesmundi.org)
Gaddafi's decision to use violence against peaceful demonstrators in Benghazi and Tripoli started a civil war in February 2011. (blog.politics.ox.ac.uk)
Seamus Burns is concerned that executive blunderbuss could blow away the rights of peaceful demonstrators (newlawjournal.co.uk)