I'll leave the in-depth analysis of President Trump's executive order on refugee policy to more competent legal minds than my own. But a few general points:
Many of the most prominent attacks on this order have been overly broad (by ignoring the historical history of refugee policy, making claims that the United States has no right to limit refugees, and so forth). While it has whipped up partisan enthusiasm, this excessive rhetoric has hurt the argument against the president's actions. If the choice becomes framed as the Trump EO v. open borders, the executive order would probably come out on top in a public opinion poll.
We need to attend to the real (not the sentimentalized) history of immigration law and refugee policy in order to see where the Trump EO breaks from standing norms and where it falls within them. Falsifying history is a dangerous political tactic.
If federal appointees can declare themselves willing to nullify duly passed laws and regulations at whim, we have not a democratic republic but anarchy.