I think that might represent a safer approacher for dealing with Muslims (as well as Christians with different doctrines than yours) than trying to determine if they represent a Satanically inspired religion.

I, for one, don't think we humans particularly need any diabolical assistance to create malicious, hateful or violent beliefs, rituals and world views; we do a pretty good job of it all by ourselves. Nor do I think I could safely discern the difference between someone who just came up with a wacky theory on their own, someone who was inspired by God but then screwed up the message, and someone who was inspired by Satan.
And really, I'm not sure dealing on the possibility of Satanically inspired religions is likely to accomplish anything other than making it harder to remember the "good people" that may be behind the bad doctrine. I went to a church once where the pastor warned against casually attributing things to Satanic influence because it tended to give the devil more than his due and, most crucially, encouraged one to dwell on the evil works of Satan rather than on the good works of God, and that's never healthy.