Taylor is correct: innocent does mean having done nothing wrong. In this sentence though, the meaning of "innocent" is slightly (but not too) different: it means "not associated in any way with" a more guilty party (in this case, it's the people who are doing what they're doing at the end of the sentence). In other words, this sentence could be rewritten as...
"Islam has no association with what they're doing."
"Islam has nothing to do with those people and their actions."
I hope my explanation was clear. Please let me know if it wasn't.