The process of entering the US with a visa is not complete until the visa holder has cleared the final interview at the Port of Entry and has been admitted to the US.
Green cards can be revoked at any time and upon returning to the US the green card holder must still satisfy the customs Agent at the Port of Entry that they do not fall into a category of aliens not allowed to enter the US. I.E.: was involved in sex tourism with children or narcotic trade, etc.
At issue here is a blanket change in policy that affected a very small number of people holding valid U.S. visas and green cards, and who were already in transit. Their paperwork got revoked, essentially, while they were in flight. That's just shabby.
If Trump wants to refuse visa applications from suspect countries until further notice, fine. (I agree.) If he wants to make any further visas contingent on much tougher screening, fine. (I agree.) If he wants to sharply reduce total numbers of legal immigrants, fine. (I agree.) If he wants to cancel the visas of foreign nationals who have not yet flown, fine -- as long as there is a reasonable notification period and a way to warn or stop them before they get on a plane. But what we should not do -- and what is causing the current ruckus -- is to allow some guy with valid papers to board a plane and fly halfway around the world, and cancel his papers while he's in transit, for reasons utterly unrelated to anything he did.
That's a mistake, even if this action can be made to stand up in court. I checked the DHS website yesterday, which said the U.S. granted entry to over 181 million foreign travelers in 2015. (I suppose the 2016 figures are not yet fully processed.) We are not a sub-Saharan gonzo clown show where nothing is certain. The world kinda, sorta expects that U.S. papers mean what they say. If we want to change policy on something, fine, but in a non-emergency situation, we should allow a reasonable notification period. The people involved in the current hoo-hah were already in transit. That should be a safe harbor -- unless, of course, we have some specific cause for concern about a particular person.
Sovereign nations have awesome powers when they choose to use them, but what I describe here would be patently unfair to you. We should not do that to a green card holder who went home to wherever to visit his family. If he stopped by at a jihadi training center to sharpen his beheading technique, and U.S. authorities have become aware of it, that's a different matter, but without any adverse information, a U.S. green card should be honored.