We all must bear the "cross" of our legacies, whether we had anything to do with them, or not... Some legacies are chosen, some not... Muslims, nor any religion/belief/sect, do not get an exclusion.
I am American born... My country is the only one in the world that has used nuclear weapons against other humans. It also has conducted some rather despicable atrocities, imho. We have inflicted country music, Michael Jackson, Brittany Spears, Disney World, Reality Television, and right-wing neo-cons on the world. Things for which I am not proud, but ashamed. However, I'm still proudly American.
I am of Native American heritage as well. And carry that legacy with me as well - the good and the bad.
I am a Christian by birth and by choice. By birth, my family is loaded with Catholics and Lutherans. By choice I'm now Episcopal. The Atrocities committed by Christianity and in the name of Christianity are countless, and I acknowledge all of them. However, I can still be doing what I can to live by the Christian teachings with as much honor and grace as I can muster.
Same is true for any Muslim. There are countless atrocities committed by Islam and in the name of Islam. Same is true for Jews, Hindus, Bhuddists, Taoists, Atheist, Frisbeetarians, whateverists, et. al. So, I do not agree with the idea of innocence because they "had nothing to do with things". Denial and complacency are irresponsible and unethical, in my small view of the universe.