Months ago, the US was an ally of Denmark and Greenland. Greenland allowed an ally to have their military stationed there, because it served both (through NATO).
From one day to the other, the US behave like an enemy. And the US behave erratically. So NATO still exists on the paper because the US haven't invaded anyone yet, but the US are behaving like enemies and threaten to invade.
Seems more than rational, from the point of view of the rest of NATO, to prepare for an invasion, but at the same time hope that NATO still exists and that the US are not actually an enemy (probably not an ally anymore, but "partner" is better than "enemy").
Or am I missing something?
It's clear that Trump acts alone in foreign policy - formal channels and structures can barely check him. However, informal resistance still appears to exist. Trump apparently still takes into account the vibes of the people he surrounds himself with into account. In a haphazard way yes, but it's clear that Trump can be swayed to some degree by those around him.
The Trump administration is not a unified bloc, and there are likely many elements that see annexing Greenland as ridiculous. However, if they lost access, then they would be forced to concede that there was something actually valuable to gain.