I don't believe that the protests didn't change the outcome of the war. I wrote in March 2003 [1] that the Iraq War "is going to be much more closely criticized than other wars in the past", and it has been.
Compared to previous wars, which went on for years and killed millions of people before anyone even noticed, the Iraq War has been dogged from the outset by scrutiny and criticism. As a result, abuses have been identified more promptly, denounced more broadly and discontinued more quickly.
Things are actually getting better, but our expectations are changing faster than our institutions are conforming, so it feels like things are getting worse.
Honestly, I agree, but there were millions of people all over the world protesting the war, and it didn't change a damn thing.