Europe has provided massive aid to Ukraine, mostly financial. Their hesitation has been committing themselves militarily to the war, which, if they did, would be a huge benefit to Ukraine. But their current level of support is still very substantial (and necessary).
Greenland isn't important because it's Greenland, it's important because taking it shatters NATO. As an attack on Denmark it's actually less important than the deathblow to an alignment that has been foundational to the world order for the last 80 years. If the US takes Greenland, the whole international order breaks down, so yes, they're taking it very seriously.
> Greenland [is] important because taking it shatters NATO.
It's even more striking to me then that the Europeans would draw the line, rather than seek some kind of Trump appeasement. Standing up to Russia in Ukraine does not affect the credibility of NATO, but standing up to Trump does.
Appeasement of aggressors has a terrible track record, both historically (Hitler, Putin) and specifically with Trump (TACO).
Danish military analyst Anders Puck Nielsen argues, IMHO convincingly, that Europe should NOT try to appease Trump, but do the opposite - escalate to de-escalate: https://www.youtube.com/watch?v=PwRsTDlqU8I
His reasoning is that Trump is a malignant narcissist, and malignant narcissists separate people into two categories: those perceived as strong, whom they admire (Putin, Xi), and weak, whom they abuse. Appeasement will only encourage further abuse. The only viable option is to show strength.
As a European myself, I will support politicians with an uncompromising approach, no matter the cost.
Greenland isn't important because it's Greenland, it's important because taking it shatters NATO. As an attack on Denmark it's actually less important than the deathblow to an alignment that has been foundational to the world order for the last 80 years. If the US takes Greenland, the whole international order breaks down, so yes, they're taking it very seriously.