He's not a muslim. He has never been a muslim. His father was a muslim but was an atheist by the time his parents met. Now, the Clinton campaign and some republicans have done a marvelous job at somehow convincing people (despite not coming out and saying it directly!) that despite all of this, he is a muslim, or at least he might be. It is completely and utterly fascinating to me that in this age of the internet and instant verification and all that, misconceptions like this float around as if we are back in 1860 and word is being passed through the hills, like a game of telephone, that Abraham Lincoln had a black grandparent or something. But that's the problem, people don't really take time to verify things they hear about, they just take it as gospel truth. It's also hard because there are innumerable websites that will feed your confusion and paranoia.
The internet, for example, will tell you convincingly that vaccines cause autism, the CIA caused the 9/11 terror attacks, Kennedy was assassinated by a conspiracy between the mafia and castro, "cleansing your colon" is the secret to good health, Elvis is still alive, Paris Hilton has talent, and not only do UFOs exist but aliens walk among us daily.