Yes, the United States should extend constitutional due process to non-citizens accused of terrorism because non-citizens are still human beings with certain inalienable rights that cannot be ignored. A non-citizen should still be granted these rights and not have them ignored purely based upon their national status or nation of origin.
I believe terrorists should have the same constitutional due process protections that citizens have because our constitution states that everyone should be subjected to a trial by jury, so that should be effective for anyone getting tried in our court systems. Even for those non citizens accused of terrorism. I believe that our founding fathers made that so because it shows how a democracy operates in courts and trials.