The very words themselves are DUE (as in required) PROCESS (as in steps to be taken, or laws to be followed). If there are no steps required to be taken to execute a citizen, you have a complete Fascist Dictatorship.
Not taking Due Process is taking the law into your own hands, the right to murder with impunity.
Due Process is taken in war between two opposed belligerent sides, both of your examples. A war is declared, and people make their choices and pay the price for it.
But in this case, there is no process at all, a citizen is thought to be helping someone who we do not have a legally declared war with, and someone somewhere can arbitrarily decide that he deserves execution. That this question can be posed is a indication of how far from the process of Justice and Law this country has fallen.
RE: A war is declared, and people make their choices and pay the price for it.
Well, we are at war with Al Qaeda and the Taliban and the terrorists.
We declared a WAR ON TERROR since 9/11. So, the belligerents who chose the side of the terrorists have made their choices. I see no reason why the should not pay the price for it.