The American constitutions, like all constitutions, applies to everyone who is on the territory of the US. Not just citizens. Not only does it not apply to non-citizens outside of the US (obviously) it also don't apply to US citizens outside of the United States (once again, pretty obvious)
Fact is that Trump's ban bans people from countries whose nationals have not killed an American citizen in a terrorist attack since, I think, 1975. Anyway, it's a badly written executive order as it is unclear and ambigious. Executive agencies had no real clear idea what they were supposed to and foreign governments had no idea whether it could apply to their immigrant citizen.
Is the ban unconstitutional? Seems so, or else the courts would not have suspended it. Trump is of course in his full right to appeal, but he openly questioned the legitimacy of the courts. Why? It doesn't help his case. It won't speed up his appeal. It certainly won't make other judges more likely to accept his actions and it certainly doesn't change anything about the wording of the Constitution. What people sorta forget is that it's the courts that decide on unconstitutionality. You can make a great case on how it is, but that doesn't change the fact that by American legislature, the Supreme Court has that final say. If they say something about the constitution, it automatically becomes law until overturned by that same court. Our interpretation of law changes overtime. Nobody felt that 'All men are created equal' applied to Negro's, women or natives when it was written. Yet that line is still there, and rights are derived from it.
Tl;dr, deciding whether it's unconstitutional is not really up to us. Deciding whether it's morally right of course is.
What pains me the most is that apparantly, allowing people that worked as translators for the US Armed Forces into the country is 'detrimental to the interests of the United States'. Why did his order not make an exception to this? Why are people who endanger the lives of themselves and their families a danger to the United States? This just feels like plain injustice, and even if you do not agree with that, then consider the fact that not harbouring these people if their lives are in danger will make it very hard for the US to find new translators or other local support.
PS: apologies for any typo's or grammar mistakes, I worked a late shift and its like 3:30 in the morning.