America was founded on principles of freedom, among them the freedom of speech, and particularly freedom of political speech. So the question of whether Americans have the right to protest against a war has the answer, "definitely, yes." However, just because one has the right to do something like protest a war doesn't mean that he or she ought to do it.
Today, the protesters send the message that Americans are not of one voice or of one mind on the Iraq war, and that has implications for how various parties respond. The enemy, as in the Vietnam War, is strengthened and emboldened. And our military personnel are confused at a time when they need the undoubted support of those of us at home.
A pretty good argument can be made that activities that embolden the enemy and call into question the degree of support for our troops are not patriotic.