You're wrong. They have no responsibility to "keep their mouths shut." In fact, they have the RIGHT to speak out.
Too many ignorant people here and elsewhere have no clue or concept of what is meant by "treason" or "sedition." It is NOT treasonous to speak your mind. It is not seditious to exercise your right of free speech.
If you and people like you are going to be so ignorant on this issue, then I invite you to refrain from EVER mentioning the Bill of Rights again.
If this idea of "it's treason to critisize the gov't during war" ever takes hold, it won't be very long before some tyrant decides that the best way to prevent dissent is to simply have a perpetual war.
And that would be far more dangerous than any words from an anti-war protestor.
BTW, on a side note, this world would be a much better place if more people throughout history had listened to anti-war protestors since the overwhelming majority of wars fought on this planet have been for the wrong reasons.
Would you like to hear my advice to any protester who is considering taking to the streets after the war has officially begun? You would? It would be something along the lines of, "Dude, watch out for a late model, white Dodge Ram with a reinforced front bumper and some Bondo on the right rear wheel well."
By the time you see me, it'll probably be too late. Peace-out.