Levings claims, "The Quran forbids Muslims to swear allegiance to the U.S. Constitution; therefore, technically, all Muslims should be refused immigration" but just as with Christianity, there are many interpretations of Islam and like Christians, Muslims are free to cherry-pick what they adhere to and what they don't as far as the doctrines of the faith are concerned. 
Technically, the government cannot use the words of the Koran to ban all members of a particular religion from the rights and protections of American laws. There are already many Americans who subscribe to the Muslim faith and the laws protect them. Politicians like Trump though seem to be trying to instigate discrimination and violence against Muslims by non-muslims especially far-Right Christian fanatics and white supremacists. The potential for violence from this political demographic is real and should be monitored by the government.