If backing down gives the enemy a new victory to proclaim over American weakness and increase their recruiting, you're fine by that? The politics of appeasement serves their interests, not ours.
Acting prudently and respectfully is not "backing down". Enciting anger is just not good tactics. Have you considered that the act of burning their holy books might just drive some into battle who have been more moderate to this point? Why not persue a course of action that is more thoughtful, respectful, and less dangerous? Would you actually act in such a way as to increase the danger to our troops, even if it was a mere remote chance that it could have some affect? I choose to take the safest approach, for I want all of those men to come home safely. My personal statements of distain or my own excercise of Free Speech seems to be worth far less than even a flesh wound for one of those guys. I would choose instead to excerise my right to Free Speech to protect those men and possibly limit the agression against them, regardless of how little my affect on that might be. Burning Muslim holy books is much more likely to have a negative affect worldwide than a positive affect, so why not just abstain for the sake of those who sit in the sand for you? Unless, of course, the well being of those men really doesn't mean anything compared to this "important" act you support.