Nothing has ever been accomplished by doing nothing. When large numbers of people gather to speak with one voice it is difficult to ignore them, even for the mainstream media, and it raises awareness. Protests also allow the anti war movement to better organize.
It is also a form of lobbying and we all know well that works with Congress. Just look at what AIPAC has done with its pro war lobbying efforts.
Lawyers who stand with the anti war movement should file suit against the Pentagon/Government for this.