Islam has no mechanism for excommunication. Individuals can leave the ummah and be regarded as apostates (murtad). But no one who swears he is a Muslim can be excluded. Even very bad Muslims are still Muslims as long as they haven't thrice publicly rejected the two testimonies. (The two testimonies are accepting the oneness of God and that Mohammed is His Prophet.) Thus, neither Obama nor anyone else is qualified to decide who is a Muslim — or what is true Islam.

Obama's elementary errors on Islam, New York Post (February 20, 2015).