While I'm pretty sure protesters do not have the explicit right to damage property, I do believe the best type of protest, is one that upholds a peaceful protest. This could possible disrupt public life, but there again, that falls, somewhat into the definition of what a protest is mean to do.
There should be a law to prevent protests from disrupting our everyday lives and to keep protesters from damaging out property. If someone is unable to get to work, pick up the kids, or get somewhere important because of protests that is harmful to the community and should be stopped.
First of all, there's absolutely no excuse whatsoever for the wanton destruction of property during protests.
Secondly, blocking freeways with extremely fast-moving vehicular traffic on them put both drivers and protestors who insist on engaging in such a tactic in danger of serious injury or death.
Thirdly, physically preventing people from getting to important medical treatment appoints for life-threatening conditions, or getting their sick or injured pets to a vet due to a life-or-death emergency is totally inexcusable, as is causing emergency vehicles to have to be diverted and making getting a seriously ill or injured person to the nearest and best hospital, or getting to the scene of a crime or fire difficult, if not impossible, is also inexcusable.
A peaceful protest is only successful in very specific conditions, and if the conditions are not right the protest will fail. Sometimes violence is necessary and justified –– when it's directed at a greater injustice. And if there's a law against non-peaceful protest there should be a protest about it.