The constitution is a set of rules for the government to live by, and a statement of American values. If we allow our government to pick and choose who to apply the values and standards to, then better hope your group isn't next.
The constitution clearly specifies persons and citizens at different points.
persons means non citizens living on american soil. there are debates over how much of the constitution should apply to non citizens on american soil or to american citizens abroad but that's not what we're dealing with here. the ability to migrate to another country is a privilege the rulers of that country give you it is not a right you are born with.
there is nothing un american about denying entry to barbarians who adhere to a supremacist totalitarian ideology and would overthrow your system in a heartbeat if they could. i'm not even talking about terrorism. they just need to outbreed you and vote to implement the sharia. muslims are 20% of the french population and they are set to be the majority of all births in sweden within a couple of years.
@spendulus sorry i forgot to include them, i see that bryant coleman has posted the isis one, here's the link to the sharia questions. the worrying thing is there's not much difference between these results and the ones that get taken in western countries.
http://www.pewforum.org/2013/04/30/the-worlds-muslims-religion-politics-society-beliefs-about-sharia/