This response isn't counter productive. Immature and childish yes. Counter productive no. It helps to point out the importance of free speech.
So does dressing up in white robes and goofy hats and marching with racial epithets on signs. The ACLU --- one of the few causes I actually donate too, despite them being unbelieveably annoying once you do --- made quite a bit deal of that. But the people doing the marching? Total counterproductive douchebags. We tolerated them. We didn't encourage them.
I don't think EDMD is congruent with a Klan march. I think a number of people consider the primary reason for EDMD to be free speech where as the primary reason for Klan marches is racism. Also you don't get to change things like the color of your skin or sexual preference where as beliefs can change. In my opinion that makes religion fair game.
I'm 110% with 'potatolicious on this. The people saying we shouldn't have to go out of our way to avoid offending Muslims are, of course, right. But there's no cause to go out of our way to offend Muslims, either.
If I was a Islamist culture-warrior, things like "Draw Muhammad Day" would be a coup for me; it might even have been the reason why I'd threaten the lives of cartoonists. To provoke a counterproductive response from the west.