It is true that you cannot be both a Muslim and a loyal American...
THEREFORE, such a person is INDEED a traitor to the American Republic and should be tried before a federal court and if found guilty subject to execution.
Proclaiming yourself a traitor and advocating sedition should be enough to start an investigation and lead to an indictment. Trials, jury, and sentencing...all the good due process is still owed to this person - if he is a citizen. If he is not a citizen, then he’s an enemy combatant without a uniform and gets no right to a trial at all.
Point being, you say you’re a traitor publicly and advocate for terrorists, you just put yourself on the no-fly list and got yourself an invitation to be questioned by the FBI.