But it is. What makes sexual intercourse wrong? What makes depicting images of your prophet wrong? They are declared wrong by your religion, fine, but if someone else does them, it doesn't affect you and your worship. No one made you watch that youtube video (if in fact you've seen it). I haven't seen it, and probably won't, simply because I have no interest in it.
Something you must understand about our American values: free speech is the right upon which all other rights are based. Without speech, there is nothing. You have the freedom to declare Muhammad the greatest prophet of all, I have the right to declare that I see no reason to believe in a God at all.
People in this country say thing I consider incredibly, horribly wrong. There are holocaust deniers, neo-nazis, Klansmen, NAMBLA members, people who fuck goats, Todd Akin, Benedict Groeschel, the list goes on. I support letting these people speak because the things I say are considered equally horrible by other people (indeed, being an atheist still carries a death sentence in some parts of the world).
Furthermore, publicly silencing ideas does not eliminate them. By not letting those with ideas you detest speak their thoughts openly, their ideas fester unchallenged, further radicalizing their believers. The more strongly you react to these people publishing stupid Muhammad videos, the more intent they will be on producing them, and the more they will hate the Muslim world for their overreaction.